Multicomponent adsorption isotherms

The multicomponent adsorption isotherms operative in displacement chromatography are described by the following equation that reflects the competitive nature of the process ... 

As have been seen above adsorption plays an important role in permeation through microporous membranes. So, single and multicomponent adsorption isotherms are required for a successful modelling of the permeation behaviour. An extensive treatment of the recent state of the art of zeolite permeation modelling is given by Van de Graaf et al. [70]. A shortened treatment follows here. 

From Eqs. (20) and (21) it follows that if is independent of concentration, binary fluxes can be predicted on the basis of single-component permeation data once the multicomponent adsorption isotherm is known. 

Explicit calculation of multicomponent adsorption isotherms of gas mixtures using the IAS theory... 

We have shown in the last few sections the LAS theory as well as its computation implementation to obtain multicomponent adsorption isotherm. Since this theory is based on solution thermodynamics it can be applied to prove the thermodynamic consistency of the extended Langmuir equation. 

The approach of IAS of Myers and Prausnitz presented in Sections 5.3 and 5.4 is widely used to calculate the multicomponent adsorption isotherm for systems not deviated too far from ideality. For binary systems, the treatment of LeVan and Vermeulen presented below provides a useful solution for the adsorbed phase compositions when the pure component isotherms follow either Langmuir equation or Freundlich equation. These expressions are in the form of series, which converges rapidly. These arise as a result of the analytical expression of the spreading pressure in terms of the gaseous partial pressures and the application of the Gibbs isotherm equation. 

The multicomponent adsorption isotherm for the component 1 is obtained by the application of the Gibbs equation ... 

The multicomponent adsorption isotherm of the second component is obtained by simply interchanging the subscripts 1 and 2 in the above equation. 

The extension of the potential theory was studied by Bering et al (1963), Doong and Yang (1988) and Mehta and Dannes (1985) to multicomponent systems. We shall present below a brief account of a potential theory put forward by Doong and Yang (1988). The approach is simple in concept, and it results in analytical solution for the multicomponent adsorption isotherm. The basic assumption of their model is that there is no lateral interaction between molecules of different types and pure component isotherm data are described by the DA equation. With this assumption, the parameters of the DA equation (Wq, Eq, n) of each species are not affected by the presence of the other species, but the volume available for each species is reduced. This means that the volume available for the species i is ... 

The experimental measurement of multicomponent adsorption isotherms is time consuming because of the large number of variables involved, and the problem of predicting binary and multicomponent equilibria from singlecomponent adsorption data has therefore attracted much attention. A brief review of the various approaches which have been followed is given in this section. For simple systems considerable success has been achieved but there is still no established method with universal proven applicability, and this problem remains one of the more challenging obstacles to the development of improved methods of process design. 

Ideal adsorbed solution theory (lAST) was used in this study because it is the most common approach used to predict the multicomponent adsorption isotherms onto activated carbon by using only single solute equilibrium data. The lAST is based on the assumption that the adsorbed mixture forms an ideal solution at a constant spreading pressure. The model can be represented by the following Equation 6.4 ... 

AH practical adsorbents have surfaces that are heterogeneous, both energetically and geometrically (not all pores are of uniform and constant dimensions). The degree of heterogeneity differs substantially from one adsorbent type to another. These heterogeneities are responsible for many nonlinearities, both in single component isotherms and in multicomponent adsorption selectivities. 

Adsorbed-Solution Theoiy The common thennodynamic approach to multicomponent adsorption treats adsorption equilibrium in a way analogous to fluid-fluid equilibrium. The theory has as its basis the Gibbs adsorption isotherm [Young and Crowell, gen. refs.], which is... 

The Langmuir Equation for the Case Where Two or More Species May Adsorb. Adsorption isotherms for cases where more than one species may adsorb are of considerable significance when one is dealing with heterogeneous catalytic reactions. Reactants, products, and inert species may all adsorb on the catalyst surface. Consequently, it is useful to develop generalized Langmuir adsorption isotherms for multicomponent adsorption. If 0t represents the fraction of the sites occupied by species i, the fraction of the sites that is vacant is just 1 — 0 where the summation is taken over all species that can be adsorbed. The pseudo rate constants for adsorption and desorption may be expected to differ for each species, so they will be denoted by kt and k h respectively. 

Mixture phase equilibrium calculations, types of, 24 680-681 Mixture-process design type, 8 399 commercial experimental design software compared, 8 398t Mixtures. See also Multicomponent mixtures Nonideal liquid mixtures acetylene containing, 2 186 adsorption, 2 593-594 adsorption isotherm models,... 

The multicomponent Langmuir adsorption isotherm given in Eq. (7) is the simplest model for the description of non-linear, multicomponent, adsorption equilibrium. At high concentration, the model predicts saturation of the stationary phase and overload of the chromatographic column. At low concentration (high dilution) the behavior can be correctly described by the non-competitive linear adsorption isotherm ... 

According to the equilibrium dispersive model and adsorption isotherm models the equilibrium data and isotherm model parameters can be calculated and compared with experimental data. It was found that frontal analysis is an effective technique for the study of multicomponent adsorption equilibria [92], As has been previously mentioned, pure pigments and dyes are generally not necessary, therefore, frontal analysis and preparative RP-HPLC techniques have not been frequently applied in their analysis. 

Moreover, they are all based on isothermal behavior and approximations of adsorption isotherms and have not been applied to multicomponent mixtures. The greatest value of these calculation methods may lie in the prediction of effects of changes in basic data such as flow rates and slopes of adsorption isotherms after experimental data have been measured of breakthroughs and effluent concentration profiles. In a multicomponent system, each substance has a different breakthrough which is affected by the presence of the other substances. Experimental curves such as those of Figure 15.14 must be the basis for sizing an adsorber. 

The problem of predicting multicomponent adsorption equilibria from single-component isotherm data has attracted considerable attention, and several more sophisticated approaches have been developed, including the ideal adsorbed solution theory and the vacancy solution theory. These theories provide useful quantitative correlations for a number of binary and ternary systems, although available experimental data are somewhat limited. A simpler but purely empirical approach is to use a modified form of isotherm expression based on Langmuir-Freundlich or loading ratio correlation equations ... 

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