Simple isothermal models, kinetic parameters

Fig. 11. Evaluation of kinetic parameters for the DOC model—CO and HC oxidation. Comparison of experimentally observed and simulated outlet concentrations in the course of the oxidation light-off for simple mixtures (a) CO, reaction Rl (b) Ci0H22, reactions R4 and R7 (cf. Table II). Lab experiments with isothermal monolith sample using synthetic gas mixtures (14% 02, 6% C02, 6% H20, N2 balance). Rate of temperature increase /min, SV = 30,000 h 1 (Kryl et al., 2005). Reprinted with permission from Ind. Eng. Chem. Res. 44, 9524, 2005 American Chemical Society.

The transient response experiments were analyzed by a dynamic isothermal PFR model, and estimates of the relevant kinetic parameters were obtained by global nonlinear regression over all runs. It was found that a simple Langmuir approach could not represent the data accurately, and surface heterogeneity had to be invoked. The best fit was obtained using a Temkin-type adsorption isotherm with coverage-dependent desorption energy ... 

There is no reqnirement that the model represent a simple reactor snch as a CSTR or isothermal PER. If necessary, the model can represent a nonisothermal PER with variable physical properties. It can be one of the distributed parameter models in Chapters 8 or 9. The model parameters can inclnde the kinetic parameters in Equations... 

For the most simple column models under certain simplifying conditions there are analytical solutions of the model equations available. Related to the equilibria this holds for problems vhere all components of interest are characterized by linear isotherm equations, in vhich the Henry constants are not affected by the presence of other component. Then all kinetic effects causing band broadening can be described by a single lumped parameter, for example, the number of theoretical plates. Consequently, the usage of two or more kinetic parameters is not justified. 

The problem of estimation of the kinetic parameters from linear FR characteristic functions, has been solved long ago, for simple isothermal kinetic models [15]. The process time constant can be estimated from the extremum of the so-called out-of-phase function [15], which is identical to the negative imaginary part of the first-order particle FRF Fi,p(o)) [28]. 

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. 

Adsorption kinetics of a single particle (activated carbon type) is dealt with in Chapter 9, where we show a number of adsorption / desorption problems for a single particle. Mathematical models are presented, and their parameters are carefully identified and explained. We first start with simple examples such as adsorption of one component in a single particle under isothermal conditions. This simple example will bring out many important features that an adsorption engineer will need to know, such as the dependence of adsorption kinetics behaviour on many important parameters such as particle size, bulk concentration, temperature, pressure, pore size and adsorption affinity. We then discuss the complexity in the dealing with multicomponent systems whereby governing equations are usually coupled nonlinear differential equations. The only tool to solve these equations is... 

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