Kinetic modeling chemical reaction processes

E. James Davis, Microchemical Engineering The Physics and Chemistry of the Microparticle Selim M. Senkan, Detailed Chemical Kinetic Modeling Chemical Reaction Engineering of the Future Lorenz T. Biegler, Optimization Strategies for Complex Process Models... 

Similar in spirit, but aimed at a very different community, is the work at Leeds, carried out jointly between the research groups of Peter Dew in computing and Mike Pilling in chemistry. One important focus here is on distributing the computational task of modelling chemical reaction processes in reaction kinetics, combustion, and... 

This involves knowledge of chemistry, by the factors distinguishing the micro-kinetics of chemical reactions and macro-kinetics used to describe the physical transport phenomena. The complexity of the chemical system and insufficient knowledge of the details requires that reactions are lumped, and kinetics expressed with the aid of empirical rate constants. Physical effects in chemical reactors are difficult to eliminate from the chemical rate processes. Non-uniformities in the velocity, and temperature profiles, with interphase, intraparticle heat, and mass transfer tend to distort the kinetic data. These make the analyses and scale-up of a reactor more difficult. Reaction rate data obtained from laboratory studies without a proper account of the physical effects can produce erroneous rate expressions. Here, chemical reactor flow models using matliematical expressions show how physical... 

The Flory principle is one of two assumptions underlying an ideal kinetic model of any process of the synthesis or chemical modification of polymers. The second assumption is associated with ignoring any reactions between reactive centers belonging to one and the same molecule. Clearly, in the absence of such intramolecular reactions, molecular graphs of all the components of a reaction system will contain no cycles. The last affirmation concerns sol molecules only. As for the gel the cyclization reaction between reactive centers of a polymer network is quite admissible in the framework of an ideal model. 

Thus there are enough uncertainties in the kinetics in most chemical reaction processes that we almost always need to resort to a simplified model from which we can estimate performance. Then, from more refined data and pilot plant experiments, we begin to refine the design of the process to specify the details of the equipment needed. 

In the preceding chapters, the theory of elementary reactions was discussed. The chemical processes occurring in chemically reacting flows usually proceed by a series of elementary reactions, rather than by a single step. The collection of elementary reactions defining the chemical process is called the mechanism of the reaction. When rate constants are assigned to each of the elementary steps, a chemical kinetic model for the process has been developed. 

Froment, G.F., Fundamental Kinetic Modeling of Complex Processes, in Chemical Reactions in Complex Mixtures The Mobil Workshop. A.V. Sapre and F.J. Krambeck, eds., Van Nostrand Reinhold, 77-100,1990. 

The premise of molecular biology is that cellular processes are governed by physico-chemical principles, and accordingly, those principles may be used to translate known or hypothetical molecular mechanisms to mathematical equations. In this section, the general principles of chemical kinetics, mass transport, and fluid mechanics used to model chemical reaction systems are reviewed briefly. 

Several types of models are commonly used to describe the dispersion of atmospheric contaminants. Among these are the box, plume, and puff models. None are suitable, however, for describing the coupled transport and reaction phenomena that characterize atmospheres in which chemical reaction processes are important. Simulation models that have been proposed for the prediction of concentrations of photochemically formed pollutants in an urban airshed are reviewed here. The development of a generalized kinetic mechanism for photochemical smog suitable for inclusion in an urban airshed model, the treatment of emissions from automobiles, aircraft, power plants, and distributed sources, and the treatment of temporal and spatial variations of primary meteorological parameters are also discussed. 

Chemical reaction processes account for the production of a variety of contaminant species in the atmosphere. Each of the basic airshed models above includes reaction phenomena in the conservative equations. The reaction term, denoted by R accounts for the rate of production of species i by chemical reaction and depends generally on the concentrations of each N species. The conservation equations are thus coupled through the Ri terms, the functional form of each term being determined through the specification of a particular kinetic mechanism for the atmospheric reactions. 

There will be instances where the use of an airshed model will be limited to the prediction of concentrations of inert species. However, when chemical reaction processes are important, it is essential to include an adequate description of these phenomena in the model. Here we outline the requirements that an appropriate kinetic mechanism must meet, survey pertinent model development efforts, and present an example of a mechanism that possesses many of the attributes that a suitable model must display. 

These considerations and the set of equations for transport of the solute through the HF modules are modified and simplified in comparison to the HFCLM [91] theoretical considerations. The models presented in Sections 13.2.1 and 13.2.2 consider more detailed diffusion parameters at the F/LM and LM/R interfaces, more detailed kinetics of chemical reactions. So, they are more identical to the real transport processes, therefore, these models, modified for a hollow-fiber permeator, may be used for the hoUow-fiber transport also. 

Takeuchi et al. 7 reported a membrane reactor as a reaction system that provides higher productivity and lower separation cost in chemical reaction processes. In this paper, packed bed catalytic membrane reactor with palladium membrane for SMR reaction has been discussed. The numerical model consists of a full set of partial differential equations derived from conservation of mass, momentum, heat, and chemical species, respectively, with chemical kinetics and appropriate boundary conditions for the problem. The solution of this system was obtained by computational fluid dynamics (CFD). To perform CFD calculations, a commercial solver FLUENT has been used, and the selective permeation through the membrane has been modeled by user-defined functions. The CFD simulation results exhibited the flow distribution in the reactor by inserting a membrane protection tube, in addition to the temperature and concentration distribution in the axial and radial directions in the reactor, as reported in the membrane reactor numerical simulation. On the basis of the simulation results, effects of the flow distribution, concentration polarization, and mass transfer in the packed bed have been evaluated to design a membrane reactor system. 

The recent research focus of CVD B4C is to reveal the deposition mechanism under different deposition conditions and establish the relationship between deposition parameter and deposition mechanism, for which thermodynamic, mass transfer and kinetic modeling attempts have been studied by several research groups". The CVD B4C from BCI3/CH4/H2 precursor is a very complex chemical reaction process, and the B4C can be deposited by different mechanisms. Some reasonable deposition mechanisms have been established, such as Thomas S. Moss et al, and Mustafa Karaman et al, their experiments were performed under a small variation of deposition parameters and thus all of the B4C deposits had similar microstriicture and phase composition, which probably suggest the B4C coatings were deposited by a single mechanism. 

In this section some basic features of nonlinear wave propagation in non-reactive and RD processes will be illustrated and compared with each other. The simulation results presented are based on simple equilibrium or non-equilibrium models [51, 65] for non-reactive separations. In the reactive case, similar models are used, assuming either kinetically controlled chemical reactions or chemical equilibrium. We focus on concentration (and temperature) dynamics and neglect fluid dynamics. Consequently, for equimolar reactions constant flows along the column height are assumed. However, qualitatively similar patterns of behavior are also displayed by more complex models [28, 57, 65] and have been confirmed in experiments [41, 59, 89, 107] for non-reactive multi-component separations. First experimental results on nonlinear wave propagation in reactive columns are presented subsequently. 

Quasi-kinetic models deal with processes that are controlled by mass transfer rates rather than by chemical reaction rates. These models assume nearly instantaneous attainment of equilibrium within the region of interest, so changes in the species distribution are controlled by the rate of transfer of substances into or out of that region. These models are constrained by continuity equations making them similar to the chemical reactors models in Chapter 4. 

Both deterministic and stochastic models can be defined to describe the kinetics of chemical reactions macroscopically. (Microscopic models are out of the scope of this book.) The usual deterministic model is a subclass of systems of polynomial differential equations. Qualitative dynamic behaviour of the model can be analysed knowing the structure of the reaction network. Exotic phenomena such as oscillatory, multistationary and chaotic behaviour in chemical systems have been studied very extensively in the last fifteen years. These studies certainly have modified the attitude of chemists, and exotic begins to become common . Stochastic models describe both internal and external fluctuations. In general, they are a subclass of Markovian jump processes. Two main areas are particularly emphasised, which prove the importance of stochastic aspects. First, kinetic information may be extracted from noise measurements based upon the fluctuation-dissipation theorem of chemical kinetics second, noise may change the qualitative behaviour of systems, particularly in the vicinity of instability points. 

We believe that the objective quantitative interpretation of the kinetics, the time evolution of a chemical reaction, has to be in harmony with generally accepted approaches for the description of system dynamics. In accordance with this intention, we used the method of the Hamiltonian systematization of kinetic models of reaction systems. At the same time, the physical-chemical, kinetic comprehension of initial mathematical characteristics enabled to come to new systemic concepts in chemical kinetics, such as the value contributions of species and individual steps, specifying their kinetic significance in miltistep processes. 

In the sections that follow, we will delve deeply into the atomistic world of reaction kinetics and learn how to predict the rates of a number of fairly simple zero, first, and second-order reaction processes. While this chapter will focus mostly on simple gas-phase chemical reaction processes, the principles learned here will apply just as well to the solid-state materials kinetic examples that we will confront later in the textbook. This is because bond-breaking and bond-forming processes are remarkably similar at the atomistic level whether they happen between molecules in the gas phase or between atoms in a solid. Thus, most reaction processes can be described using a common set of approaches. Toward the end of the chapter, in preparation for later solid-state applications of reaction kinetic principles, we will examine how reaction rates can be affected by a catalyst or a surface, and we will learn how to model several gas-solid surface reaction processes relevant to materials science and engineering. 

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