On reactor design for complex systems of first-order chemical reactions

The mathematical problems of reactor design and performance depend primarily on the solution of a set of partial differential or difference equations. These equations are linear if the reactions are first-order, if temperature variations are not significant, and if mass transfer by diffusion obeys Fick's law. When a reactor problem can be solved for a single irreversible first-order reaction, it can also be solved for a system of coupled first-order reactions of any number of chemical species and of arbitrary complexity.     

Kinetic models of complex reaction systems

In this work, the desired N-oxidation of β-picoline (3-methylpyridine), 2,6-lutidine, 3,5-lutidine and 2,4,6-collidine and the undesired hydrogen peroxide decomposition accompanying the syntheses reactions have been studied by means of reaction calorimetry. The power generation measurements have been used for the development of a kinetic model that will represent satisfactorily the N-oxidation of this family of reactions and it can be used towards the prediction of selected runaway scenarios of the respective reactions. Their kinetic study was based on the kinetic model of Sempere et al. [Sempere, J., Nomen, R., Rodriguez, J. L., & Papadaki, M. (1998). Modelling of the reaction of 2-methylpyridine using hydrogen peroxide and a complex metal catalyst. Chemical Engineering and Processing, 37, 33–46.], which was improved and refined. It was found that the model represents well the N-oxidation of methylpyridines. Due to limited miscibility of di- and trimethylpyridines with hydrogen peroxide, water and catalyst only partial agreement with the model was achieved. These reactions need further study under conditions where homogeneous mixtures can be formed. A simple methodology was employed for the evaluation of the model coefficients. Accurate evaluation of the kinetic model constants can be achieved if the noise of measurements is reduced, or conditions where it is less pronounced are employed.     

Selectivity analysis in electrochemical reactors. II. Engineering models of a batch reactor with a complex reaction sequence

This paper presents a mathematical model of a batch stirred-tank electrochemical reactor where a required cathodic reduction reaction is coupled with a complex reaction sequence between the reactant and the key product. The set of coupled, non-linear differential equations is solved numerically and simple dimensionless quantities characterizing the cell performance and selectivity are derived. The experimental results presented in Part I of this paper are found to be in excellent agreement with the model. In the particular case where the homogeneous chemical reactions may be neglected in the cathodic diffusion boundary layer, a simplified analytical expression of the process selectivity is proposed. This quantifies the effects of the operating conditions by means of a single dimensionless criterion.     

Mathematical models for a packed-bed chemical reactor

Various approaches to the mathematical representation of the simultaneous phenomena of heat transfer, mass transfer, and chemical reaction, within a packed-bed chemical reactor, are summarized and discussed from the point of view of both accuracy and practicality. After careful analysis of the ideas presented in the recent literature, a relatively simple unidimensional model is proposed for use, both for steady-state calculations and for dynamic analysis. The assumptions inherent in the use of the proposed model are carefully stated, and areas of uncertainty are pointed out. Reference is made to recent work in which the proposed model has found application.     

Yield optimization for complex reactor systems

For complex reactions, the choice of reactor type is important for attaining optimum product yields. Strategies for specifying reactor types have beenIn this paper, product yield in a Van de Vusse reaction scheme has been studied for a wide range of the rate constants, in a reactor system consisting     

Semi-Markovian models of the functioning of complex chemical engineering systems

This article deals with the general approaches to the construction of semi-Markovian models of chemical engineering systems. The basic lines of development of the semi-Markovian modeling apparatus, used for the determination of the rational set of measures to ensure the models’ economically efficient functioning, are shown. Expressions for the characterization of the maintenance service system and the repair of complex chemical engineering facilities are suggested.     

甲醇制烯烃反应动力学及反应器模型研究进展

甲醇制烯烃（MTO）工艺是现代煤化工领域的研究热点,MTO反应动力学及其反应器模型研究是高效反应器开发和工业装置操作优化的基础。本文综述了甲醇制烯烃反应动力学研究进展,详细论述了机理型动力学模型、八集总动力学模型、五集总动力学模型,指出集总动力学模型适用于描述MTO反应过程,如何考虑水、积炭等因素的影响是MTO动力学研究的难点和关键。结合现有动力学模型,评述了MTO反应过程在工业规模的固定床反应器、提升管反应器、循环流化床反应器、湍动流化床反应器中产物分布和转化率模拟情况,结果表明：循环流化床反应器和湍动流化床反应器适合MTO工业过程。最后指出,甲醇制烯烃反应动力学下一步研究方应集中于工业规模流化床反应器气固两相流动模拟,以及与动力学模型结合获得准确预测工业反应结果的MTO反应器模型。     

Required levels of catalysis for emergence of autocatalytic sets in models of chemical reaction systems

The formation of a self-sustaining autocatalytic chemical network is a necessary but not sufficient condition for the origin of life. The question of whether such a network could form "by chance" within a sufficiently complex suite of molecules and reactions is one that we have investigated for a simple chemical reaction model based on polymer ligation and cleavage. In this paper, we extend this work in several further directions. In particular, we investigate in more detail the levels of catalysis required for a self-sustaining autocatalytic network to form. We study the size of chemical networks within which we might expect to find such an autocatalytic subset, and we extend the theoretical and computational analyses to models in which catalysis requires template matching.     

Mass transfer with mth order chemical reaction for multi-particle systems

The steady-state diffusion equation with convective term and mth order chemical reaction term was numerically solved by the finite difference method. The penetration theory agreed only with the numerical solution around single spheres in an infinite potential flow field. The enhancement factor varies with the values of the Reynolds number, void fraction and contamination factor.     

Understanding and optimization of chemical reactor performance for bimodal reaction sequences

The relative contributions of heterogeneously catalyzed and homogeneous bulk phase reactions in bimodal reaction sequences have been assessed via 1D reactor simulations. Starting from a reaction network only comprising two parallel, irreversible heterogeneously catalyzed and homogeneous bulk phase steps, complementary consecutive steps were included with the option of being reversible. The final product formed after a minimum number of homogeneous bulk phase reactions is obtained with high yields in continuous flow fixed bed reactors. The products obtained after a higher number of homogeneous bulk phase reactions generally dominate in slurry reactors. Yields of the latter may exhibit an optimum as a function of the catalyst amount in the reactor. The adsorption enthalpies of the intermediates in the reaction network critically determine the position and shape of this maximum. The reversibility of the homogeneous bulk phase steps provides specific opportunities to tune the product yields in bimodal reaction sequences. © 2016 American Institute of Chemical Engineers AIChE J, 63: 111–119, 2017     

Mathematical reactor modelling for coupled chemical and electrochemical processes: the ECE system

A procedure for modelling electrochemical reactions and reactors which involve heterogeneous reaction, homogeneous fast chemical reaction and diffusional mass transport is described. The procedure can be applied to any combination of first order reaction processes utilising numerical routines for the solution of initial value differential equations. By the use of collocation it can be extended to higher order processes. The reactor types considered are batch, plug flow and dynamic continuous stirred tanks and reactors with recycle. Operation with either potentiostatic, galvanostatic or constant cell voltage control is described and illustrated using the ECE reaction mechanism, involving successive electrochemical, chemical and electrochemical reaction.     

Variant and invariant states for chemical reaction systems

Models of chemical reaction systems can be quite complex as they typically include information regarding the reactions, the inlet and outlet flows, the transfer of species between phases and the transfer of heat. This paper builds on the concept of reaction variants/invariants and proposes a linear transformation that allows viewing a complex nonlinear chemical reaction system via decoupled dynamic variables, each one associated with a particular phenomenon such as a single chemical reaction, a specific mass transfer or heat transfer. Three aspects are discussed, namely, (i) the decoupling of reactions and transport phenomena in open non-isothermal both homogeneous and heterogeneous reactors, (ii) the decoupling of spatially distributed reaction systems such as tubular reactors, and (iii) the potential use of the decoupling transformation for the analysis of complex reaction systems, in particular in the absence of a kinetic model.     

Valid parameter range analyses for chemical reaction kinetic models

The present work quantifies the relations between the structure of a chemical reaction kinetic model, its valid parameter range, and the truncation error tolerance of the model. General methods are presented to solve the three important problems of valid parameter range analysis: (1) identification of the valid parameter range of a kinetic model, (2) estimation of the error tolerance required when applying a kinetic model over a specified parameter range, and (3) improvement of existing model generation algorithms to construct more robust models. Finally, the relationship between a model's structure, its valid parameter range, and the truncation error tolerance are illustrated by the flexibility-tolerance-model graph. The new methods are applied to pyrolysis of methane/ethane mixtures.     

Multiphase CFD-based models for chemical looping combustion process: Fuel reactor modeling

Chemical looping combustion (CLC) is a flameless two-step fuel combustion that produces a pure CO₂ stream, ready for compression and sequestration. The process is composed of two interconnected fluidized bed reactors. The air reactor which is a conventional circulating fluidized bed and the fuel reactor which is a bubbling fluidized bed. The basic principle is to avoid the direct contact of air and fuel during the combustion by introducing a highly-reactive metal particle, referred to as oxygen carrier, to transport oxygen from the air to the fuel. In the process, the products from combustion are kept separated from the rest of the flue gases namely nitrogen and excess oxygen. This process eliminates the energy intensive step to separate the CO₂ from nitrogen-rich flue gas that reduce the thermal efficiency.Fundamental knowledge of multiphase reactive fluid dynamic behavior of the gas-solid flow is essential for the optimization and operation of a chemical looping combustor.Our recent thorough literature review shows that multiphase CFD-based models have not been adapted to chemical looping combustion processes in the open literature. In this study, we have developed the reaction kinetics model of the fuel reactor and implemented the kinetic model into a multiphase hydrodynamic model, MFIX, developed earlier at the National Energy Technology Laboratory. Simulated fuel reactor flows revealed high weight fraction of unburned methane fuel in the flue gas along with CO₂ and H₂O. This behavior implies high fuel loss at the exit of the reactor and indicates the necessity to increase the residence time, say by decreasing the fuel flow rate, or to recirculate the unburned methane after condensing and removing CO₂.     

Incremental identification of kinetic models for homogeneous reaction systems

An incremental approach for the identification of stoichiometries and kinetics of complex homogeneous reaction systems is presented in this paper. The identification problem is decomposed into a sequence of subproblems. First, the reaction fluxes for the various species are estimated on the basis of balance equations and concentration measurements stemming from isothermal experiments. This task represents an ill-posed inverse problem that requires appropriate regularization. Using target factor analysis, suitable reaction stoichiometries can then be identified. In a further step, the reaction rates are estimated without postulating a kinetic structure. Finally, the kinetic laws, i.e., the dependencies of the reaction rates on concentrations, are constructed by selecting the best model structure from a set of model candidates. This incremental approach is shown to be both efficient and flexible for utilizing the available process knowledge. The methodology is illustrated on the industrially relevant acetoacetylation of pyrrole with diketene.     

多种复杂化学反应动力学统一的数值模拟

研究各种经典复杂化学反应动力学方程如简单级次反应、平行反应、连续反应和对峙反应等的求解方法时,可以发现它们之间存在共同点,并得到统一的求解形式.文中给出了将多种复杂化学反应动力学的求解统一起来的方法,并用C++程序语言,编制了可以求解物理化学教学中各种经典复杂化学反应动力学方程的数值模拟程序.使用该程序,只要根据具体情...     

Gas absorption with zero-order chemical reaction in a foam-bed reactor

A mathematical model for oxidation of aqueous alkaline solution of sodium dithionite using air as an oxidizing medium in a foam-bed reactor has been developed under pseudo-zero-order conditions of reaction and was found to be in good agreement with the experiments. Reactor conditions were 30°C at atmospheric pressure and surfactant used in the foam contactor was octyl phenoxy polyethoxyethanol (Triton X-100). The results of simulation for concentration profiles of the dissolved gas-phase reactant inside foam film based on above model are presented for different gas flow rates, reaction rates, and times of contact. The effects of variables such as superficial gas velocity and initial liquid-phase reactant concentration on conversion are also studied and compared with experiments on oxidation of sodium dithionite. The results indicate that the conversion increases with the increase in the superficial air velocity and initial dithionite concentration. The model predicts the experimentally obtained conversions reasonably well.