Adsorption ideal adsorbed solution theory

Ideal Adsorbed Solution Theory. Perhaps the most successful approach to the prediction of multicomponent equiUbria from single-component isotherm data is ideal adsorbed solution theory (14). In essence, the theory is based on the assumption that the adsorbed phase is thermodynamically ideal in the sense that the equiUbrium pressure for each component is simply the product of its mole fraction in the adsorbed phase and the equihbrium pressure for the pure component at the same spreadingpressure. The theoretical basis for this assumption and the details of the calculations required to predict the mixture isotherm are given in standard texts on adsorption (7) as well as in the original paper (14). Whereas the theory has been shown to work well for several systems, notably for mixtures of hydrocarbons on carbon adsorbents, there are a number of systems which do not obey this model. Azeotrope formation and selectivity reversal, which are observed quite commonly in real systems, ate not consistent with an ideal adsorbed... 

Isotherm Models for Adsorption of Mixtures. Of the following models, all but the ideal adsorbed solution theory (lAST) and the related heterogeneous ideal adsorbed solution theory (HIAST) have been shown to contain some thermodynamic inconsistencies. References to the limited available Hterature data on the adsorption of gas mixtures on activated carbons and 2eohtes have been compiled, along with a brief summary of approximate percentage differences between data and theory for the various theoretical models (16). In the following the subscripts i and j refer to different adsorbates. 

Crittenden. J.C., Luft, P.. Hand. D.W., Oravitz, J.F., Loper, S.W., and Ari, M. Prediction of multi-component adsorption equilibria using ideal adsorbed solution theory. Environ. Sci Technol, 19(11) 1037-1044,1985. 

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 ... 

A novel and simple method for determination of micropore network connectivity of activated carbon using liquid phase adsorption is presented in this paper. The method is applied to three different commercial carbons with eight different liquid phase adsorptives as probes. The effect of the pore network connectivity on the prediction of multicomponent adsorption equilibria was also studied. For this purpose, the Ideal Adsorbed Solution Theory (lAST) was used in conjuction with the modified DR single component isotherm. The results of comparison with experimental data show that incorporation of the connectivity, and consideration of percolation processes associated with the different molecular sizes of the adsorptives in the mixture, can improve the performance of the lAST in predicting multicomponent adsorption equilibria. 

In general, the model can represent the experimental data fairly well as seen in Figure 3. The adsorption isotherms for the other binary systems on Filtrasorb-400, and Norit ROW 0.8 are available elsewhere [9]. In order to test the importance of the incorporation of the pore network connectivity concept, the ideal adsorbed solution theory was also applied without considering the connectivity of the pore network. For this purpose, we also used the binary... 

The effect of the pore network connectivity on the prediction of binary adsorption equilibria is studied. The Ideal Adsorbed solution theory (lAST) is used in conjunction with modified DR single component isotherm, and it is found that incorporation of the connectivity... 

Ideal adsorbed solution theory (lAST) [4] is a widely used engineering thermodynamic method, the equivalent to the Raoult s law for adsorption, which uses the pure-gas isotherms as inputs to predict the mixture adsorption equilibrium at the temperature of interest. Before the lAST calculation, the pure gas isotherm must be fitted with a suitable isotherm equation to an acceptable degree of accuracy we used a piece-wise fit [3]. 

A multicomponent HSDM for acid cfye/carbon adsorption has been developed based on the ideal adsorbed solution theory (lAST) and the homogeneous surface diffusion model (H SDM) to predict the concentration versus time decay curves. The lAST with the Redlich-P eterson equation is used to determine the pair of liquid phase concentrations, Q and Qj, from the corresponding pair of solid phase concentrations, q j and q jy at fha surface of the carbon particle in the binary component. 

This study firstly aims at understanding adsorption properties of two HSZ towards three VOC (methyl ethyl ketone, toluene, and 1,4-dioxane), through single and binary adsorption equilibrium experiments. Secondly, the Ideal Adsorbed Solution Theory (IAST) established by Myers and Prausnitz [10], is applied to predict adsorption behaviour of binary systems on quasi homogeneous adsorbents, regarding the pure component isotherms fitting models [S]. Finally, extension of adsorbed phase to real behaviour is investigated [4]. 

Predictions of adsorption equilibria by ideal-adsorbed-solution theory are usually satisfactory when the specific amount adsorbed is less than a third of the saturation value for mono-layer coverage. At higher adsorbed amounts, appreciable negative deviations from ideality are promoted by differences in size of the adsorbate molecules and by adsorbent heterogeneity. One must then have recourse to Eq. (14.123). The difficulty is in obtaining valnes of the activity coefficients, which are strong functions of both spreading pressnre and temperatnre. This is in contrast to activity coefficients for liquid phases, which for most applications are insensitive to pressure. This topic is treated by Talu et ai. ... 

Gas mixture adsorption is a field that is still waiting for a better theory to explain the experimental data. The Ideal Adsorbed Solution Theory cannot explain aU the facts and needs to be replaced by a new model that includes nonideal effects, and adsorbent surface heterogeneity in particular. This field is acquiring increasing relevance because of its technological impHcations. 

Richter, E., Schiitz, W., and Myers, A.L. (1989). Effect of adsorption equation on prediction of multicomponent adsorption equilibria by the ideal adsorbed solution theory. Chem. Eng. Sci., 44, 1609-16. 

Fundamentals of sorption and sorption kinetics by zeohtes are described and analyzed in the first Chapter which was written by D. M. Ruthven. It includes the treatment of the sorption equilibrium in microporous sohds as described by basic laws as well as the discussion of appropriate models such as the Ideal Langmuir Model for mono- and multi-component systems, the Dual-Site Langmuir Model, the Unilan and Toth Model, and the Simphfied Statistical Model. Similarly, the Gibbs Adsorption Isotherm, the Dubinin-Polanyi Theory, and the Ideal Adsorbed Solution Theory are discussed. With respect to sorption kinetics, the cases of self-diffusion and transport diffusion are discriminated, their relationship is analyzed and, in this context, the Maxwell-Stefan Model discussed. Finally, basic aspects of measurements of micropore diffusion both under equilibrium and non-equilibrium conditions are elucidated. The important role of micropore diffusion in separation and catalytic processes is illustrated. 

Besides the switching time, the feed concentration is the most important parameter for enhancing productivity of an SMB process. The shape and the location of the region of complete separation in a (m, m3)-diagram are mainly influenced by the feed concentration. Therefore, the feed concentration for the simulation was gradually increased. Quadratic Hill-adsorption isotherms dependent on pressure were determined for the phytol-isomers. The mixture interactions were taken into account by the ideal adsorbed solution theory (lAST) [58). 

The multiphase ideal adsorbed solution theory (MIAST) is another model of the family of adsorbed solutions. Corrtraiy to HAST, an energy distribution function is assumed with differences of the local or molectrlar site energy. Therefore, every site has its own local adsorption isotherm arrd the adsorbate concentration differs from site to site. The adsorbate is not considered as a homogeneous phase but as a multiphase system. 

Recognizing the deficiency of the extended Langmuir equation, despite its sound theoretical footing on basic thermodynamics and kinetics theories, and the empiricism of the loading ratio correlation, other approaches such as the ideal adsorbed solution theory of Myers and Prausnitz, the real adsorption solution theory, the vacancy solution theory and the potential theory have been proposed. In this section we will discuss the ideal adsorbed solution theory and we first develop some useful thermodynamic equations which will be used later to derive the ideal adsorbed solution model. 

Eqs. (5.3-lOb) and (5.3-12) define the ideal adsorbed solution theory. The surface potential, (j), is calculated from the Gibbs adsorption isotherm equation (Bering et al., 1970) ... 

A brief qualitative evaluation of CO2 adsorption selectivity in MOFs is the direct observation on differences in uptakes between separated gases under given conditions, usually based on the single-component adsorption isotherms. These isotherms can also be used to quantitatively estimate the adsorption selectivity. If adsorption species are presented at low loadings, namely within the Henry s regime, the adsorption selectivity for an equimolar mixture is close to the ratio of the Henry s constants for each species. At non-dilute loadings, however, more information is required to estimate multi-component adsorption. One common approach is to use ideal adsorbed solution theory (lAST) to predict multi-component adsorption isotherms and selectivity based on the single-component adsorption isotherms [60], This approximate theory is known to work accurately in many porous materials. 

In the past 30 years, great efforts have been expended to develop techniques for predicting the multicomponent adsorption equilibria based on pure component data. However, until now only limited success has been achieved. Several publications provide good reviews of the work in this area [1,2,5]. Generally speaking, these models can be classified into four groups (1) Vacancy solution theory, (2) statistical models, (3) ideal adsorbed solution theory (lAST), (3) Polanyi theory, and (4) various empirical or semiempirical models,... 

Among the theories of predicting mixed-gas adsorption equilibria from pure component adsorption isotherms, the ideal adsorbed solution theory (IAST) [14] has become the standard and often serves as a benchmark for the purpose of comparison by other models. IA ST is a thermodynamically rigorous theory based on the mixing of individual components at constant spreading pressure to form an ideal solution. It has the advantages that (1) no mixture data are required and (2) the theory is independent of the actual model of physical adsorption. 

FIGURE 4.21. X-Y diagram for adsorption of O2-CO on lOX zeolite at 144 K, 760 torr, showing comparison of experimental data of Danner and Wenzel (O), with theoretical predictions of ideal adsorbed solution theory (—), vacancy solution theory without sorbate-... 

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