Kinetic model single components

Al-Duri, B., and McKay, G., Comparison in theory and application of several mathematical models to predict kinetics of single component batch adsorption systems. Process Safety Environ. Prot., 68(4), 254-268 (1990). Chen, Y.D. Ritter, J.A., and Yang, R.T., Nonideal adsorption from multicomponent gas mixtures at elevated pressures on a 5A molecular sieve, Chem. Eng. Sci.. 45(9), 2877-2894 (1990). 

This model was shown to be applicable for describing moisture uptake kinetics (in vacuum) above RH0 for single-component systems of alkali halides, sugars, and choline salts [31]. The model later was extended to consider the moisture uptake kinetics above RH0 for multicomponent systems of these substances [33]. 

If the assumptions made above are not valid, and/or information about the rate constants of the investigated reactions is required, model-based approaches have to be used. Most of the model-based measurements of the calorimetric signal are based on the assumption that the reaction occurs in one single step of nth order with only one rate-limiting component concentration in the simplest case, this would be pseudo-first-order kinetics with all components except one in excess. The reaction must be carried out in batch mode (Vr = constant) in order to simplify the determination, and the general reaction model can, therefore, be written as Equation 8.14 with component A being rate limiting ... 

A general kinetic model should accommodate all chemical processes known to affect the dechlorination process. These include (1) reductive dechlorination takes place on the iron surface, rather than in the aqueous phase, so adsorption must occur (2) other components in the system may affect the dechlorination reaction by competing for the reaction sites (3) surface sites for reduction and for sorption may not be the same, as for the system with PCE and TCE where dechlorination takes place on the reactive sites, but most of the adsorption is clearly on the nonreactive sites (Burris et al., 1995). In the following section we will first discuss a single-site model similar to the one used by Johnson et al. (1998), which has accounted for the first two observations, then develop a two-site model that will also take the third observation into consideration. We aim to illustrate how coadsorbates in the iron system will affect adsorption and reduction of chlorinated solvents. TCE will be used as an example since relevant adsorption and reduction data are available, from which the required parameters for simulation could be estimated. 

Kinetic mechanisms involving multiple reactions are by far more frequently encountered than single reactions. In the simplest cases, this leads to reaction schemes in series (at least one component acts as a reactant in one reaction and as a product in another, as in (2.7)-(2.8)), or in parallel (at least one component acts as a reactant or as a product in more than one reaction), or to a combination series-parallel. More complex systems can have up to hundreds or even thousands of intermediates and possible reactions, as in the case of biological processes [12], or of free-radical reactions (combustion [16], polymerization [4]), and simple reaction pathways cannot always be recognized. In these cases, the true reaction mechanism mostly remains an ideal matter of principle that can be only approximated by reduced kinetic models. Moreover, the values of the relevant kinetic parameters are mostly unknown or, at best, very uncertain. 

Pressure Swing Adsorption (PSA) unit is a dynamic separation process. In order to create a precise model of the process and thus an accurate design, it is necessary to have a good knowledge of the mixture s adsorption behaviour. Consequently, the dilAision rates in the adsorbent particles and the mixture isotherms are extremely vital data. This article intends to present a new approach to study the adsorption behaviour of isomer mixtures on zeolites. In a combined simulation and experimental project we set out to assess the sorption properties of a series of zeolites. The simulations are based on the configurational-bias Monte Carlo technique. The sorption data are measured in a volumetric set-up coupled with an online Near Infra-Red (NIR) spectroscopy, to monitor the bulk composition. Single component isotherms of butane and iso-butane were measured to validate the equipment, and transient volumetric up-take experiments were also performed to access the adsorption kinetics. 

Having obtained the adsorption equilibrium and mass transfer parameters of single component systems (Tables 1 to 2), we are ready to examine the predictability of the model in simulating the sorption kinetics of multicomponent systems on Norit activated carbon. 

In linear chromatography, these last two linear kinetic models are particular cases of the model used by Lapidus and Amundson [85] (Eq. 2.22). By contrast, the different lumped kinetic models give different solutions in nonlinear chromatography. Investigations of the properties of these models and especially of the relationship between the band profiles and the value of the kinetic constant have been carried out for many single-component problems. Numerous studies of the influence of the mass transfer kinetics on the separation of binary mixture have been published in the last ten years. These results are discussed in Chapters 14 and 16, respectively. 

All cases of practical importance in liquid chromatography deal with the separation of multicomponent feed mixtures. As shown in Chapter 2, the combination of the mass balance equations for the components of the feed, their isotherm equations, and a chromatography model that accounts for the kinetics of mass transfer between the two phases of the system permits the calculation of the individual band profiles of these compounds. To address this problem, we need first to understand, measure, and model the equilibrium isotherms of multicomponent mixtures. These equilibria are more complex than single-component ones, due to the competition between the different components for interaction with the stationary phase, a phenomenon that is imderstood but not yet predictable. We observe that the adsorption isotherms of the different compounds that are simultaneously present in a solution are almost always neither linear nor independent. In a finite-concentration solution, the amount of a component adsorbed at equilib-... 

For single-component systems, the theoretical solutions obtained are easy to compare to experimental profiles. They differ only by the smoothing effect due to axial dispersion and to the finite kinetics of mass transfers in actual columns. In many cases, because of the qualities of the stationary phases currently available, these effects appear to be secondary compared to the major role of thermodynamics in controlling the band proffles in overloaded elution. Admittedly, the influence of the finite coliunn efficiency on the band profiles prevents a successful quantitative comparison between theoretical and experimental band profiles. However, these profiles are similar enough at high concentrations and the solutions of the ideal model indicate which are the trends to be expected. 

Furthermore, the theoretical analysis of the single-component problem in the ideal model provides some of the fimdamental concepts in nonlinear chromatography, such as the notions of the velocity associated with a concentration, of concentration shocks, and of diffuse bormdaries [1,2]. It also provides an understanding of the relationship between the thermod5mamics of phase equilibria, the shape of the isotherm (i.e., convex upward, linear, convex downward, or S-shaped) and the band profiles. Finally, it provides an explanation of the relative importance of the influences of the thermodynamics and the kinetics on the band profile. These concepts will provide a most useful framework for imderstanding the phenomena that occur in preparative chromatography. 

The Thomas model [23] is the only kinetic model that has an analytical solution in the single-component case, in nonlinear chromatography. In all other cases, the... 

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