Steam reforming of methanol over a CuO/ZnO/Al2O3 catalyst, part I: Kinetic modelling

A kinetic study of the methanol steam reforming reaction was performed over a commercial CuO/ZnO/Al₂O₃ catalyst (Süd-Chemie, G66 MR), in the temperature range of 200–300 °C. The reactions considered in this work were methanol steam reforming (MSR) and reverse water gas shift (rWGS). Several MSR kinetic rate models developed by different authors were compared and the one was determined that best fitted the experimental data. A kinetic Langmuir–Hinshelwood model was proposed based on the work by Peppley et al. (1999a) . The kinetic expressions that presented the best fit were used to simulate the packed bed reactor with a one-dimensional model. A good agreement between the mathematical model and the experimental data was observed.     

Two-phase modeling of a gas phase polyethylene fluidized bed reactor

A two-phase model is proposed for describing the behavior of a fluidized bed reactor used for polyethylene production. In the proposed model, the bed is divided into several sequential sections where flow of the gas is considered to be plug flow through the bubbles and perfectly mixed through the emulsion phase. Polymerization reactions occur not only in the emulsion phase but also in the bubble phase. Voidages of the emulsion and bubble phases are estimated from the dynamic two phase structure hydrodynamic model. The kinetic model employed in this study is based on the moment equations. The hydrodynamic and kinetic models are combined in order to develop a comprehensive model for gas-phase polyethylene reactor. The results of the model are compared with the experimental data in terms of molecular weight distribution and polydispersity of the produced polymer. A good agreement is observed between the model predictions and actual plant data. It has been shown that about 20% of the polymer is produced inside the bubble phase and as such cannot be neglected in modeling such reactors.     

A homogeneous chemical reactor analysis and design laboratory: The reaction kinetics of dye and bleach

An experimental module for senior-level reaction engineering/reactor design students is described. The module is used to characterize the kinetics of dye (food coloring) neutralization by household bleach, and the reactor system is configurable for use in either batch reactor or continuous-stirred tank reactor (CSTR) modes. The reactor temperature, volume, reactant feed rates, and reactant concentrations may be adjusted to enable students to obtain a wide range of kinetic data. Dye concentrations in the reactor are monitored by absorbance spectroscopy, and the kinetic rate law is determined directly from the batch reactor performance data. Students use the completed kinetic rate law to compare experimental steady-state CSTR performance data to the mathematical models derived from reactor design equations. Finally, the students use the kinetic behavior of the system to design a hypothetical plug-flow reactor for the same chemical reaction and a set of stated operational goals.     

Gas-liquid autoxidation reactors

A procedure for the simulation of autoxidation gas-liquid reactors has been developed based both on mathematical models and laboratory experiments. It has been shown that the complex radical chain mechanism of the autoxidation process can be simulated through two global parallel reactions, whose rates are obtained by assuming pseudo-steady-state concentration values for all the radical species involved. Using ethylbenzene autoxidation as a model reaction, an experimental analysis has been performed in order to estimate all the kinetic parameters of the model. The effect of the interaction between gas-liquid mass-transfer phenomena and the complex kinetic mechanism on the overall performance of an autoxidation reactor has been examined in detail within the framework of the liquid film model.     

生物质流化床空气-水蒸气气化模型研究

根据流化床反应器特点,结合生物质气化动力学反应机理,建立了生物质在流化床内气化的等温稳态、一维二相动力学模型。该模型所做的主要假定如下:流化床分为气泡相和乳相,在气泡相和乳相内均存在化学反应,考虑二相内的轴向气体扩散,生物质热解过程瞬时完成,主要考虑焦碳以及CO,CO2,H2,H2O,CH4等在流化床内发生的8个主要化学反应。数学模型属于常微分方程组边值问题,利用数值计算软件M atlab7.0进行编程求解。以木粉为原料,将模型结果与实验结果进行了对比,模拟结果与试验数据符合良好,在一定程度上证明了模型的有效性和可靠性。     

The kinetics of complex catalytic reactions

The mathematical and statistical tools for parameter estimation and model discrimination in complex kinetic models are briefly reviewed. Hougen-Watson type rate equations are extended to simultaneous reactions and to situations in which the active site concentration varies through the reactor as a consequence of changes in the gas phase composition. Examples are given of the kinetic modeling of processes based upno complex feedstocks. Lumping of components and reactions, as well as partitioning of the networks are illustrated. Finally, the benefit of expressing rates in terms of truly elementary mechanisms is discussed.     

MODELING OF GAS OIL CATALYTIC CRACKING IN A FIXED BED REACTOR USING A FIVE-LUMP KINETIC MODEL

A five-lump kinetic model had been developed for modeling of gas oil catalytic cracking. The experiments were carried out in a standard fixed bed micro-activity test (MAT) reactor. Distribution of the cracking product components was determined as a function of temperature. The sequential step optimization method was used to estimate the kinetic constants. A MAT reactor nonisothermal and the unsteady-state model was proposed. The overall heat of the reactions was established from the macroscopic difference of the products' and the reactants' enthalpies. The influence of the feedstock and the reactor temperature was discussed. The reactor and the kinetic models were validated using the experimental MAT results. Simulation results were in good agreement with the experimental data.     

Optimal reaction conditions for the minimization of energy consumption and by‐product formation in a poly(ethylene terephthalate) process

We determined the optimal reaction conditions to minimize the energy cost and the quantities of by‐products for a poly(ethylene terephthalate) process by using the iterative dynamic programming (IDP) algorithm. Here, we employed a sequence of three reactor models: the semibatch transesterification reactor model, the semibatch prepolymerization reactor model, and the rotating‐disc‐type polycondensation reactor model. We selectively chose or developed the reactor models by incorporating experimentally verified kinetic models reported in the literature. We established the model for the entire reactor system by connecting the three reactor models in series and by resolving some joint problems arising when different types of reactor models were interconnected. On the basis of the simulation results of the reactor system, we scrutinized the cause and effect between the reaction conditions and the final quality of the polymer product. Here, we set up the optimization strategy by using IDP on the basis of the integrated reactor model, and the process variables with significant influence on the properties of polymer were selected as control variables with the help of a simulation study. With this method, we could refine the reaction conditions at the end of each iteration step by contracting the spectra of control regions, and the iteration process finally stopped when the profile of the optimal trajectory converged. We also took the constraints on the control variables into account to guarantee polymer quality and to suppress side reactions. Constituting six different strategies by setting weighting vectors differently, we examined the differences in optimal trajectories, the trend of optimality, and the quality of the final polymer product. For each of the strategies, we conducted the optimization to examine whether the number‐average degree of polymerization approached the desired value. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 993–1008, 2002     

Flow-rate effects in flow-reversal reactors: experiments, simulations and approximations

Design and operation of a reactor with flow reversal requires accurate prediction of the domain of operating conditions, and especially the range of flow rates, where the ignited state exist. In this work we compare experimental observations of flow-rate effects during ethylene oxidation on Pt/Al₂O₃, with simulations of this reactor using a kinetic rate expression that was derived elsewhere and with approximate solutions based on instantaneous or very fast reactions. The oxidation of ethylene on supported Pt catalyst, that is employed here as a model reaction, is a complex reaction characterized by self-inhibition (expressed by Langmuir-Hinshelwood kinetics), by strong activation energy and by strong thermal effects that lead to a wide domain of steady-state multiplicity. The analysis of a flow- reversal reactor for such reactions can be approximated using the assumption of an instantaneous or fast reaction as the feed meets the catalyst layer. We suggest several approximations that capitalize on this property and apply them to the structure of our reactor, in which the catalytic bed is imbedded between two inert zones.Adequate agreement between the experimental results and simulations, using homogeneous or heterogeneous reactor model with no adjustable parameters, is demonstrated. The difference between the homogeneous and heterogeneous model predictions is usually small. The approximations show that the most important parameters for predicting the highest temperature are the inert zone properties (conductivity and length).     

Kinetic analysis utilizing a recirculating flow reactor system

A system which recirculates reactants from a stirred vessel through a remote reactor is described. Highly reproducible kinetic measurements are achieved for liquid phase reactions in general and those requiring isolation in particular. Typical reactions which require isolation involve high pressure, intense radiation, explosive mixtures, etc. The conversion history within the vessel is related to reaction rate through a mathematical model which facilitates interpretation of kinetic data. The stirred vessel is modeled as a perfectly uniform reservoir coupled to the arbitrary reaction element by two transfer lines modeled as time delays. The analysis includes the effects of a parabolic velocity profile attendant to the use of low circulation rates or high viscosities. Analytical solutions are obtained for limiting cases and the model system simulated on an analog computer. The results are compared to experimental data on a radiation induced vinyl polymerization     

Precise parameter estimation for chemical batch reactions in heterogeneous medium

A sequential experimental strategy for precise parameter estimation has been used in the case of liquid-liquid dispersions in batch-stirred tank reactors where slow chemical reactions take place. The mathematical model for a batch reaction in a stirred tank reactor is formulated as a system of non-linear differential equations standing for the mass balance of each component. Physical kinetic parameters and chemical kinetic parameters which arise from this model are estimated simultaneously. The estimation problem is posed as a weighted least squares problem and solved by using a standard Levenberg-Marquardt algorithm. In this work, we intend to show how it is possible to develop efficient experimental design strategies that lead to an accurate estimation of the parameters involved in phenomenological models and most particularly in kinetic models. Three design criteria for designing the experiments have been employed in order to increase the precision on the parameter estimates of the model. A standard non-linear sequential quadratic programming method ensures the determination of the operating conditions which define the experimental design. The well-known alkaline hydrolysis of esters in aqueous phase has been treated as a numerical application example.     

膜控制氧化反应器中丁烯氧化脱氢的研究

在气体均布的无机膜控制氧化反应器上进行了丁烯氧化脱氢制丁二烯反应,并将其与固定床方式反应的实验结果进行了对比,结果表明在实验范围内膜反应器比传统的固定床反应更为有效。建立了描述控制氧化膜反应器操作性能的数学模型,并将模型求解值与实验值对比,吻合良好。     

Modeling and simulation for acrylamide polymerization of super absorbent polymer

In view of the scale up of a batch reactor for super absorbent polymer (SAP), a dynamic mathematical model of a commercial scale batch reactor was developed with mass balance, energy balance, and complex polymerization kinetics. The kinetic parameters of the polymerization were estimated on the basis of the established mathematical model and reference data. Simulation results were validated with less than 10% marginal error compared with reference data. A case study was executed in terms of dynamic simulation for eight different initial concentrations of initiator and monomer to analyze the influence of initial concentration and predict the operation condition for desired product. The results were compared with various reference data, and good agreement was achieved. From the results, we argue that the methodology and results from this study can be used for the scale up of a polymerization batch reactor from the early stage of design.     

A kinetic study of the electrochemical hydrogenation of ethylene

In this study, we have examined the kinetics of the electrochemical hydrogenation of ethylene in a PEM reactor. While in itself this reaction is of little industrial interest, this reaction can be looked upon as a model reaction for many of the important hydrogenation processes including the refining of heavy oils and the hydrogenation of vegetable oils.To study the electrochemical hydrogenation of ethylene, several experimental techniques have been used including polarization measurements, measurement of the composition of the exit gases and potential step, transient measurements. The results show that the hydrogenation reaction proceeds rapidly and essentially to completion. By fitting the experimental transient data to the results from a zero-dimensional mathematical model of the process, a set of kinetic parameters for the reactions has been obtained that give generally good agreement with the experimental results. It seems probable that similar experimental techniques could be used to study the electrochemical hydrogenation of other unsaturated organic molecules of more industrial significance.     

Study of the runaway characteristics of suspension polymerisation of styrene

The safe operation of a batch polymerisation reactor assumes sufficient knowledge about all the possible reactions. An investigation has been made in order to predict, with the aid of a mathematical model based on a detailed reaction mechanism, the runaway ability of a styrene batch suspension polymerisation reactor. The results of the simulation were compared with the experimental data obtained from a bench-scale test cell.     

A mathematical model of a spouted bed gasifier

A mathematical model of the spouted bed gasifier has been constructed based on simplified first order reaction kinetics for the gasification reactions and the stream tube hydrodynamic model of Mathur and Lim. This two region model treats the spout as an isothermal plug flow reactor with cross flow into a series of streamtubes forming the annulus. Each streamtube is considered as a plug flow reactor. The effects of kinetic and hydrodynamic parameters on model predictions are illustrated, and a comparison made with experimental gas composition profiles obtained in a 0.30-m dia. gasifier.     

Inferential sensors for estimation of polymer quality parameters: Industrial application of a PLS-based soft sensor for a LDPE plant

Low-density polyethylene (LDPE) and ethylene vinyl acetate (EVA) copolymers are produced in free radical polymerization using reactors at extremely high pressure. The reactors require constant monitoring and control in order to minimize undesirable process excursions and meet stringent product specifications. In industrial settings, polymer quality is mainly specified in terms of melt flow index (MI) and density. These properties are difficult to measure and usually unavailable in real time, which leads to major difficulty in controlling product quality in polymerization processes. Researchers have attempted first principles modeling of polymerization processes to estimate end use properties. However, development of detailed first principles model for free radical polymerization is not a trivial task. The difficulties involved are the large number of complex and simultaneous reactions and the need to estimate a large number of kinetic parameters. To overcome these difficulties, some researchers considered empirical neural network models as an alternative. However, neural network models provide no physical insight about the underlying process. We consider data-based multivariate regression methods as alternative solution to the problem. In this paper, some recent developments in modeling polymer quality parameters are reviewed, with emphasis given to the free radical polymerization process. We present an application of PLS to build a soft-sensor to predict melt flow index using routinely measured process variables. Issues of data acquisition and preprocessing for real industrial data are discussed. The study was conducted using data collected form an industrial autoclave reactor, which produces LDPE and EVA copolymer using free radical polymerization. The results indicated that melt index (MI) can be successfully predicted using this relatively straightforward statistical tool.     

Practical problems in the modelling of chemical reactions in fixed bed reactorsPraktische probleme bei der beschreibung von chemischen reaktionen in festbettreaktoren

Establishing a reaction rate model consists of the following steps: experimental design, evaluation of experimental results, choice of main components and main reaction steps, choice of a mathematical model for the test reactor and the rate equations and parameter identification. It will be shown that each of the above steps requires a number of decisions and assumptions which limit the general validity and extrapolability of the resulting model. In particular there is a strong interrelation of the rate equation and the underlying model of the reactor in which the kinetic experiments are performed.The restricted extrapolability requires discrimination between two different ways of using mathematical models. For design purposes, models are required which have the character of interpolations between experiments rather than that of extrapolations. In the second category models are used for speculative extrapolations to gain a better qualitative understanding of the complex interactions of transport and reaction. This in turn provides a base for decisions among rival options in chemical reaction engineering research and development.The purpose of this paper was to provide a critical review of the different steps that lead to the formulation of a reaction rate model. It was shown that each step forces a number of assumptions and decisions and this limits the general validity and extrapolability of the resulting rate model. In particular, the strong interrelations of the rate equation and the underlying reactor model are pointed out. This means that reliable simulation results can only be expected if the rate model has been determined in the same kind of reactor that is to be simulated and if the simulation results have the character of interpolations between the underlying experiments rather than extrapolations.However, even in ranges where the model results have the character of speculative extrapolations, modelling has proven an important tool in reaction engineering. Since the model results are quantified and fulfil at least the basic laws of heat and mass conservation, they can serve as guidelines for the complex interrelations of heat and mass transport and reaction in industrial reactors. It is with these guidelines at hand that decisions about alternative options for research and development in chemical reaction engineering can be put on a sound base.     

MATHEMATICAL MODELING OF NON-CATALYTIC LIQUID-SOLID REACTION AND ITS SOLUTION BY ORTHOGONAL COLLOCATION

The mathematical model of non-catalytic liquid-solid diffusion reactions discussed in this paper can be applied to quite different cases. The models in the literature such as unreacted shrinking core model, two stage model and homogeneous model can be considered as special cases of the above model which has been derived for leaching vanadium from steel slag with sodium carbonate and]or sodium bicarbonate solution reacting with two components in the slag simultaneously. The vanadium leaching reaction is inhibited by the solid product formed during the reaction. The power law equation can be used to represent the kinetic experimental data of leaching reaction. The model equations have been solved by orthogonal collocation and semi-implicit Runge-Kutta method. The parameters of the model have been estimated by the complex method. The calculated results based on this model is in good agreement with experimental data.     

不同曳力模型及颗粒碰撞恢复系数对短接触旋流反应器内气固流场的影响

为考察曳力模型和颗粒碰撞恢复系数对短接触旋流反应器内流动特性的影响,基于双流体模型, 结合颗粒动力学理论,对反应器内气固两相流场进行模拟研究。分别采用Gidaspow、Wen & Yu和Syamlal-O’Brien 3种曳力模型, 考察颗粒速度特性以及固含率径向分布。对比分析不同曳力模型的计算结果表明,Syamlal-O’Brien模型计算结果与实验结果误差较大,Wen & Yu模型在反应器边壁附近区域的计算结果误差较大,Gidaspow模型计算结果与实验结果最为吻合。此外,颗粒碰撞恢复系数较小时,所得计算值小于实验测量值,当恢复系数为0.95时颗粒扩散效果最好,计算结果与实验数据吻合度最高。