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     

Pattern formation in models of fixed-bed reactors

This work reviews and compares spatiotemporal patterns in three models of adiabatic fixed catalytic beds for reactions with oscillatory kinetics: homogeneous and heterogeneous models, which are studied using generic first-order kinetics, and a detailed model of CO oxidation in the monolithic reactor. These three models describe reactors with one, two or all three phases (fluid-, solid- and adsorbed-phases), respectively. Pattern selection is based on the oscillatory or bistable nature of the kinetics and on the nature of fronts. The heterogenous and detailed models may exhibit local bistability while the homogeneous model does not admit this property: a simple conversion between the parameters of the homogeneous and heterogeneous models is suggested.

The spatiotemporal patterns in the reactor can be predicted from the sequence of phase planes spanned by the reactor. Stationary or oscillatory front solutions, oscillatory states that sweep the whole surface or excitation fronts may be realized in the homogeneous and heterogeneous models. The detailed model of the converter may exhibit oscillatory motion, which may be periodic or chaotic, in which typically a hot domain enters the reactor exit and moves quickly upstream; the following extinction occurs almost simultaneously due to strong coupling by convection.     

Spatiotemporal patterns in models of cross-flow reactors

We review the behavior of stationary and moving spatially periodic patterns in a simple cross-flow fixed-bed reactor with a first-order exothermic reaction subject to the Danckwert’s boundary conditions and realistically high Le and Pe. Spatiotemporal patterns emerge due to the interaction of concentration and temperature balances, much like dynamic patterns in a CSTR. Moving waves emerge in an unbounded system, but they transform into stationary spatially inhomogeneous patterns in a bounded system above certain Pe threshold. The critical parameters of this threshold are derived analytically. A weakly nonlinear analysis is used in order to derive the governing amplitude equation.

The spatial behavior in the bounded system with Pe →∞ is analogous to the temporal behavior of the simple thermokinetic CSTR problem and the behavior of the distributed system is classified according to that of the lumped one. Both regular kinetics and oscillatory one (with reversible catalytic activity) are considered. Suggestions for experimental realization of these phenomena are discussed.     

Stationary and traveling hot spots in the catalytic combustion of hydrogen in monoliths

In the course of catalytic combustion of hydrogen (1-5% H₂ in air) in monolith reactors, strongly localized stationary and traveling hot spots arise in response to a sudden and persistent rise of gas flow velocity. Such hot spots may occur, e.g. in a catalytic converter following the acceleration of a car or in a catalytic combustor as a result of a load increase. This phenomenon is illustrated by simulations using a two-phase reactor model. The temperature overshoot of the adiabatic limit is typically of the order of the adiabatic temperature rise itself.The following mechanism underlies this behavior. Light fuel is supplied to the catalytic wall by fast diffusion (in the direction perpendicular to flow), while the heat released by reaction is removed from the wall by the slower, mixture-averaged heat conduction. This leads to accumulation of heat at the catalytic surface that eventually saturates at high temperatures. The hot spots may exhibit intricate dynamics, propagating downstream or upstream, or they may remain stationary. The direction of propagation depends on the relative strength of convective downstream and conductive upstream contributions to the overall displacement of reaction fronts. Generally, the hot spot tends to drift downstream at low flow velocities, remain stationary at intermediate flow velocities, and drift upstream at high flow velocities.     

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.     

热动力学法研究间歇反应器中酶促反应动力学

用热动力学法研究了间歇反应器中单底物酶促反应动力学,并详细讨论了产物竞争性抑制作用对反应速率的影响.用微量热法研究了过氧化氢酶催化分解过氧化氢和精氨酸酶催化水解L-精氨酸的反应,实验验证了本文热动力学法研究间歇反应器中单底物酶促反应动力学的正确性.     

Comparison of the performance of a direct-contact bubble reactor and an indirectly heated tubular reactor for solar-aided methane dry reforming employing molten salt

A theoretical approach is presented for the comparison of two different atmospheric pressure reactors—a direct-contact bubble reactor (DCBR) and an indirectly heated tubular reactor (IHTR)—to evaluate the reactor performance in terms of heat transfer and available catalytic active surface area. The model considers the catalytic endothermic reactions of methane dry reforming that proceeds in both reactors by employing molten salts at elevated temperatures (700–900 °C) in the absence of catalyst deactivation effects. The methane conversion process is simulated for a single reactor using both a reaction kinetics model and a heat transfer model. A well-tested reaction kinetics model, which showed an acceptable agreement with the empirical observations, was implemented to describe the methane dry reforming. In DCBR, the heat is internally transferred by direct contact with the three phases of the system: the reactant gas bubbles, the heat carrier molten salts and the solid catalyst (Ni-Al₂O₃). In contrast, the supplied heat in the conventional shell-and-tube heat exchanger of the IHTR is transferred across an intervening wall. The results suggest a combination system of DCBR and IHTR would be a suitable configuration for process intensification associated with higher thermal efficiency and cost reduction.     

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     

Classification of spatio-temporal patterns in charging and discharging of Li-ion batteries

We classify the dynamic patterns that emerge in charging or discharging of Li-ion batteries, under galvanostatic conditions, using simulations of the two-phase one-dimensional (1D) porous electrode model. This work examines the effect of the exchange current function, R₀(X), which expresses the nature of kinetics. This extends our previous study with R₀ = 1 where the same pattern emerges in charging or discharging, whether as a homogeneous or a step-wise process made of multiple symmetry breaking events. With commonly-used asymmetric R₀(X), the emerging patterns may be one of the two above or as fronts that follow single SB event and the lithiation/delithiation behaviors are different. These effects are clear when parameters are uniform; nonuniformity leads to noise that mask the behavior. The full four-variable model exhibits SB, even in absence of noise, since the liquid potential gradient (${\varphi }_l$) works like a perturbation. This similarity allows us to derive approximations to the full model behavior.     

Titanosilicate ETS-10 as a Lewis acid catalyst in the Meerwein–Ponndorf–Verley (MPV) reaction

The potential of ETS-10 as a Lewis acid catalyst was investigated using the MPV reaction at one atmosphere total pressure and 273 K. ETS-10 was hypothesized to be a potential Lewis acid catalyst as it has titanium in octahedral symmetry, which is the symmetry shown in zeolite Beta to be the most active site for the Lewis acid catalyzed Meerwein–Ponndorf–Verley (MPV) reaction. The MPV reaction is a hydrogen transfer reaction that can be used for obtaining information about the structure and performance of catalysts by comparing the product selectivities and catalytic activities. Due to their similar structures, the catalytic activity of ETS-10 was compared to zeolite Beta samples that were space-grown (flight, fewer defects) and to their earth-grown terrestrial controls. The higher tr-alcohol selectivity (i.e., trans-4-tert-butylcyclohexanol, ∼80% vs. 40%) observed over ETS-10 was attributed to a larger volume being available in the pores of ETS-10 compared to the zeolite Beta samples. By-product formation (i.e., 4-tert-butylcyclohexene) was significantly less over ETS-10 (∼5%) in comparison with the zeolite Beta samples (flight and control; ∼35%). These results reaffirm the octahedral symmetry as the Lewis active site for the MPV reaction, and illustrate that ETS-10 is a good catalyst for MPV type reactions.     

分子尺度反应动力学模型构建在催化裂化/裂解过程中的应用进展

随着环保法规的日益严格和成品油质量标准的持续升级,对催化裂化/裂解过程的产品要求和控制逐渐精细到分子级别,可靠的分子尺度反应动力学模型是实现催化裂化/裂解过程分子管理的关键所在。本文简述了催化裂化/裂解的反应机理和反应类型,回顾了近三十年来不同方法对催化裂化/裂解过程反应网络和分子尺度反应动力学模型构建的研究进展。重点对不同模型构建技术的优缺点进行了详细的对比分析,指出了催化裂化/裂解过程分子尺度反应动力学模型构建的研究方向：开发更为精细的石油分子分析表征技术,构建与催化剂失活和反应器模型相结合的分子尺度反应动力学模型,实现基于分子管理的催化裂化/裂解过程反应器设计和工艺工程放大。此外,指出建立对分子集构建、反应网络构建和动力学参数求解的集成化平台是分子尺度反应动力学发展的必然趋势。     

Phenylacetylene hydrogenation in a three-phase catalytic packed-bed reactor: experiments and model

A mathematical model was developed for the cocurrent operation of a three-phase catalytic packed-bed reactor under both trickling- and pulsing-flow regimes. The local fluctuations of liquid-solid mass transfer, liquid flow rate, and liquid holdup in unsteady pulsing-flow were simulated as periodic square-wave functions. The transport properties employed in the model were obtained using published correlations, while expressions for the intrinsic reaction kinetics were taken from our previous work. The model results were found to be in good agreement with experimental data obtained from a laboratory-scale reactor, and verified the advantage of pulsing-flow operation over trickling-flow.     

挡板偏心度对振荡流反应器三维流场对称性影响的研究

借助商业计算流体力学软件CFX,运用有限容积法离散振荡流反应器（OFR）的单个腔室,对具有理想对称几何边界和轻微挡板偏心度的OFR在系列振荡雷诺数（Reo）下的三维流场进行了仿真模拟,并将其可视化计算流场与实验流场进行比较,研究了OFR几何边界上的非对称因素对其内三维流场流型的影响.模拟结果表明在有效消除计算随机误差以及误差积累的情况下,几何边界理想对称OFR内的三维层流流场呈现出良好的中心对称性和周向均匀性,而湍流流场中心对称的同时呈现出周向非均匀结构--在圆周上生成8个中心对称排列的横向漩涡,其形态与Couette流中的泰勒涡类似.另外,挡板偏心度对OFR内的振荡流场的对称性有重要影响：在较大的下,其三维流场生成非对称性显著的大尺度漩涡对;并且随的增大,流场的非对称程度加大而增加.     

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.     

Dynamic shear in continuous-flow rotating-disk catalytic reactors with stress-sensitive kinetics based on Curie's theorem in non-equilibrium thermodynamics

Stress-sensitive response is simulated in a modified parallel-disk reactor that implements steady and unidirectional dynamic shear in the creeping flow regime. Reactants chemisorb on the surface of the rotating plate, and catalytic sites are replenished from the bulk fluid via radial and tangential flow accompanied by transverse diffusion in the z-direction toward the active surface. Chemical reaction is enhanced by viscous shear at the interface between the bulk fluid and the rotating plate. This heterogeneous catalytic rotational reactor is modeled via radial convection and axial diffusion with angular symmetry in cylindrical coordinates. The reaction/diffusion boundary condition on the surface of the rotating plate accounts for stress-sensitive reactant consumption via the zr- and zΘ-elements of the velocity gradient tensor at the catalytic surface. Linear transport laws in chemically reactive systems that obey Curie's theorem predict the existence of cross-phenomena between scalar reaction rates and the magnitude of the second-rank velocity gradient tensor, selecting only those elements of ?v experienced by reactants that are chemisorbed on the surface of the rotating plate. Stress sensitivity via the formalism of irreversible thermodynamics introduces a zeroth-order contribution to heterogeneous consumption rates that must be quenched when reactants or active vacant sites are not present on the surface of the rotating plate. Rotating-disk reactor simulations are presented for simple 1st-order, simple 2nd-order, and complex heterogeneous stress-free kinetics, where the latter considers Langmuir-type dissociative adsorption of one of the reactants. Accurate design of rotating-disk reactors must consider stress-sensitivity when the shear-rate-based Damköhler number (i.e., ratio of the stress-dependent zeroth-order consumption rate relative to the rate of reactant diffusion toward the active surface) is greater than its threshold value which increases at higher stress-free Damköhler numbers. Modulated rotation of the catalytically active plate demonstrates that these rotating-disk reactors must operate above a threshold for the stress-sensitive Damköhler number, identified under steady shear conditions, before dynamic shear has a distinguishable effect on reactor performance.     

芳烃催化加氢交叉流反应器模型

提出了一种抗硫中毒的芳烃加氢催化反应器模型,称之为交叉流反应器模型,把反应物料分为两股,其中含有噻吩的乙苯物料采用轴向连续流动方式由反应器进口进入催化剂床层,而氢气由铅直导管直接进入催化剂床层中,然后与乙苯物料混合。在氢气导管出口处形成含硫乙苯浓度低而氢气浓度高的特殊区域,因而硫对催化剂的中毒效应大幅度降低,整体上提高了乙苯加氢饱和反应效率。与传统轴向混合流反应器进行比较,在相同条件下交叉流反应器具有更好的整体加氢反应性能。分别建立了交叉流反应器与传统轴向混合流反应器模型,提出了两种反应器的催化反应转化率方程;利用此转化率方程,对实验数据进行处理,得到动力学参数,模型的计算结果与实验数据相吻合,也验证了在交叉流反应器中,硫的中毒效应明显减弱。     

Analysis of centrifugal annular reactor with radial flow

A model for centrifugal annular catalytic reactor is presented. The gas flows radially through the annulus while the inner cylinder is rotated to produce the centrifugal effect. A catalytic consecutive reaction takes place at the external surface of the annulus. The reactor is aimed to utilize the fact that heavier substances concentrate on the external walls of rotating reactors more than the lighter ones, so as to improve the conversion and yield of the desired intermediate product in consecutive reactions.The reaction performance is examined for various reaction kinetics, angular velocity and gas flow rate. The gas flow direction (inward or outward) is aIt is shown that for a given reaction and reactor geometry, an optimal angular velocity exists, where the reaction conversion is maximum. It is also sh     

Oscillations in catalytic reactions on the nm scale

We present Monte Carlo simulations of the oscillatory kinetics of CO oxidation on catalytic metals in the case when the reaction is accompanied by the formation of surface oxide. The lattice size is varied from 50 × 50 to 3 × 3 in order to mimic nm catalyst particles. More or less regular oscillations are found for the sizes down to 15 × 15. This revised version was published online in July 2006 with corrections to the Cover Date.     

Catalytic dehydration of glucose to 5‐hydroxymethylfurfural with a bifunctional metal‐organic framework

Glucose conversion to 5‐hydroxymethylfurfural (HMF) generally undergoes catalytic isomerization reaction by Lewis acids followed by the catalytical dehydration to HMF with Brönsted acid. In this work, a sulfonic acid functionalized metal‐organic framework MIL‐101(Cr)‐SO₃H containing both Lewis acid and Brönsted acid sites, was examined as the catalyst for γ‐valerolactone‐mediated cascade reaction of glucose dehydration into HMF. Under the optimal reaction conditions, the batch heterogeneous reaction gave a HMF yield of 44.9% and selectivity of 45.8%. Reaction kinetics suggested that the glucose isomerization in GVL with 10 wt % water follows the second‐order kinetics with an apparent activation energy of 100.9 kJ mol^?1. Continuous reaction in the fixed‐bed reactor showed that the catalyst is highly stable and able to provide a steady HMF yield. This work presents a sustainable and green process for catalytic dehydration of biomass‐derived carbohydrate to HMF with a bifunctional metal‐organic framework. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4403–4417, 2016     

The effects of alumina and silica nanoparticles on the cure kinetics of bisphenol E cyanate ester

Nanoparticles can be used as fillers to reinforce polymers, forming nanocomposites with better thermomechanical properties than composites with macrosized fillers. Furthermore, the addition of nanoparticles may influence the curing behavior of the polymer matrix during processing. In this study, the effect of various loadings of alumina or silica nanoparticles on the cure kinetics of bisphenol E cyanate ester (BECy) is investigated by differential scanning calorimetry (DSC). Alumina nanoparticles are shown to have a catalytic effect on the cure of BECy. The greater catalytic effect of alumina nanoparticles, compared with silica, is attributed to the increased number of hydroxyl groups on the surface and the Lewis acidity of γ‐phase alumina. Kinetic parameters were obtained from dynamic DSC experiments. For an autocatalytic model of the cure process, the kinetic parameters obtained from the model suggest that the addition of alumina nanoparticles changed the cure reaction mechanism of BECy. POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers