Reaction Kinetic Models

Solutions were obtained, either analytically or numerically, on a computer. The quenched-reaction, kinetic model considered that the nucleation sequence of reactions evolves to some time (the quenching time) and then promptly halts. Both kinetic models yield a result having the same general form as the statistical model, namely,... 

Reaction kinetics model combined with mixing model... 

All trap-spectroscopic techniques that are based on thermal transport properties have in common that the interpretation of empirical data is often ambiguous because it requires knowledge of the underlying reaction kinetic model. Consequently, a large number of published trapping parameters—with the possible exception of thermal ionization energies in semiconductors—are uncertain. Data obtained with TSC and TSL techniques, particularly when applied to photoconductors and insulators, are no exceptions. 

In order to quantify diffiisional effects on curing reactions, kinetic models are proposed in the literature [7,54,88,95,99,127-133]. Special techniques, such as dielectric permittivity, dielectric loss factor, ionic conductivity, and dipole relaxation time, are employed because spectroscopic techniques (e.g., FT i.r. or n.m.r.) are ineffective because of the insolubility of the reaction mixture at high conversions. A simple model, Equation 2.23, is presented by Chem and Poehlein [3], where a diffiisional factor,//, is introduced in the phenomenological equation, Equation 2.1. 

From the reaction-kinetic modeling point of view, the NSRC, sometimes called lean NOx trap (LNT) or NOx adsorber, is the most complex of the currently used automobile exhaust converters. A variety of different physical and chemical processes and the number of gas and surface components participating in typical periodic lean/rich operation form a large and closely linked system. 

Examples of the results obtained with the spatially ID model utilizing global NSRC kinetics are given in Figs. 26-33. The reaction kinetic model was validated with real exhaust measurement data from passenger car and heavy-duty commercial vehicle to ensure applicability in the full range of operating conditions encountered. The kinetic equations and the parameters were kept constant for all validation calculations. 

Although Fenton (1894) studied the violet color in caustic alkali during oxidation of tartaric and racemic acids by ferrous salt and hydrogen peroxide, no reaction kinetic model was offered. Fenton reported that the color disappeared when acid was added. Also, it has been observed that fresh external air is more active than room air. Fenton performed different experiments using various amounts of ferrous and hydrogen peroxides and... 

Yanagida, H., Masubuchi, Y., Minagawa, K., Ogata, T., Takimoto, J.I., and Koyama, K., A reaction kinetics model of water sonolysis in the presence of a spin trap, Ultrasonics Sonochemistry, 5, 133-139, 1999. 

Figure 3 shows a comprehensive C02 capture process model, which involves thermophysical property and reaction kinetic models for C02... 

Figure 6.72 Predicted TTT behavior for an epoxy using a first order reaction kinetic model.

Construct a time-temperature-transformation diagram for a thermoset that follows a second order reaction kinetic model described by... 

You are to pultrude a thin fiber reinforced epoxy plate at arate of lcm/s. Assume kinetic properties given in the last two problems and that the material is best represented with the autocatalytic second order reaction kinetic model of the previous problem. You are asked to design the die and the process to manufacture this product. 

Information with respect to the kinetics of a reaction may be established from DTA and DSC output by determining the fraction of reactant transformed and then fitting these data to reaction kinetics models. Modeling will be dealt with in later sections for now, we will only show how to determine the fraction of material transformed, based on a DSC/DTA trace. If we assume that the heat released per unit time is proportional to the rate of the reaction, then the partial area swept under the peat divided by the entire peat area is the fraction transformed ... 

The two-site reaction kinetics model proposed by Bonn [1] was used to evaluate the kinetic parameters. Activation energies and pre-exponential factors were determined from experiments between 570-630 K at 10 MPa. In order to decrease the strong inter-correlation between pre-exponential factors and activation energies, the reparametrisadon method of Kittrell [4] was used. Values for the pre-exponential factors at a reference temperature and activation energies are presented in Table 2. Experimental and theoretical details on HDM reaction kinetics will be published elsewhere [5]. 

Figure 5 shows the simulation of the reaction kinetic model for VO-TPP hydro-demetallisation at the reference temperature using a Be the network with coordination 6. The metal deposition profiles are shown as a function of pellet radius and time in case of zero concentration of the intermediates at the edge of the pellet. Computer simulations were ended when pore plugging occurred. It is observed that for the bulk diffusion coefficient of this reacting system the metal deposition maximum occurs at the centre of the catalyst pellet, indicating that the deposition process is reaction rate-determined. The reactants and intermediates can reach the centre of the pellet easily due to the absence of diffusion limitations. 

For example, when we consider the design of specialty chemical, polymer, biological, electronic materials, etc. processes, the separation units are usually described by transport-limited models, rather than the thermodynamically limited models encountered in petrochemical processes (flash drums, plate distillations, plate absorbers, extractions, etc.). Thus, from a design perspective, we need to estimate vapor-liquid-solid equilibria, as well as transport coefficients. Similarly, we need to estimate reaction kinetic models for all kinds of reactors, for example, chemical, polymer, biological, and electronic materials reactors, as well as crystallization kinetics, based on the molecular structures of the components present. Furthermore, it will be necessary to estimate constitutive equations for the complex materials we will encounter in new processes. 

The effectiveness factor for a wide range of reaction kinetic models differs little from that of the first-order case. For an isothermal particle, the first-order reaction effectiveness factor is... 

This last item is important because it leads to an easy way to accommodate the molar contraction of the gas as the reaction proceeds. The program calculates steady-state profiles of each of these down the length of the tubular reactor, given the reaction kinetics models, a description of the reactor and catalyst geometries, and suitable inlet gas flow-rate, pressure and composition information. Reactor performance is calculated from the flow-rate and composition data at the reactor outlet. Other data, such as the calculated pressure drop across the reactor and the heat of reaction recovered as steam, are used in economic calculations. The methods of Dixon and Cresswell (7) are recommended for heat-transfer calculations. 

In simple cases, when the number of byproducts is small, it may be possible to develop a mechanistic model of the reaction kinetics that predicts the rate of formation of the main product and byproducts. If such a model is fitted to experimental data over a suitably wide range of process conditions, then it can be used for process optimization. The development of reaction kinetics models is described in most reaction engineering textbooks. See, for example, Levenspiel (1998), Froment and Bischoff (1990), and Fogler (2005). 

Surface Reaction Kinetics-Based Models. The basic consideration in reaction kinetics models is that the reaction rate is determined by the lattice strueture on the surface. The difference in the lattice structures of various crystal planes gives rise to differences in surface bond density, electron density, surface free energy, and so on, which then determine the dissolution rate of the surface silicon atoms. All etching... 

Solution of the Reaction-Kinetic Model in the Case of a Step Injection.670... 

The same approaches that were successful in linear chromatography—the use of either one of several possible liunped kinetic models or of the general rate model — have been applied to the study of nonlinear chromatography. The basic difference results from the replacement of a linear isotherm by a nonlinear one and from the coupling this isotiienn provides between the mass balance equations of the different components of the mixture. This complicates considerably the mathematical problem. Analytical solutions are possible only in a few simple cases. These cases are limited to the band profile of a pure component in frontal analysis and elution, in the case of the reaction-kinetic model (Section 14.2), and to the frontal analysis of a pure component or a binary mixture, if one can assume constant pattern. In all other cases, the use of numerical solutions is necessary. Furthermore, in most studies found in the literature, the diffusion coefficient and the rate constant or coefficient of mass transfer are assumed to be constant and independent of the concentration. Actually, these parameters are often concentration dependent and coupled, which makes the solution of the problem as well as the discussion of experimental results still more complicated. 

The kinetics of adsorption-desorption is rarely slow in preparative chromatography, and most examples of a slow kinetics are foimd in bioaffinity chromatography, or in the separation of proteins. Thus, there are few cases in which a reaction-kinetic model is appropriate. This model is important, however, because there are many cases where it is convenient to model the finite rate of the mass transfer... 

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