Adsorbed Solution Theory

If the adsorbed phase is thermodynamically ideal, it is possible to derive the equilibrium relationships for an adsorbed mixture directly from the pure-component isotherms using the methods outlined in Section 3.4 without postulating a specific model for the adsorbed phase. For an ideal binary systenr Eq. (3.49) becomes 

Integration of the pure-component isotherm according to the Gibbs equation [Eq. (3.50)] yields, for each component, the relationship between spreading pressure and equilibrium pressure  

Prediction of the mixture isotherm in this way requires experimental singlecomponent isotherm data for the less strongly adsorbed species up to pres- 

FIGURE 4.20. Calculation of mixture adsorption equilibria from pure-component spreading pressures.  

Myers and Prausnilz CO-02 C2H4-C02 C3HS-C3H, Silica gel Active carbon Silica gel 

Adsorbed-Solution Theory The common thermodynamic 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 

Equation (16-36) with y, = 1 provides the basis for the ideal adsorbed-solution theory [Myers and Prausnitz, AIChE /., 11, 121 (1965)]. The spreading pressure for a pure component is determined by integrating Eq. (16-35) for a pure component to obtain 

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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. 

Consider a binary adsorbed mixture for which each pure component obeys the Langmuir equation, Eq. (16-13). Let n = 4 mol/kg, nl =. 3 mol/kg, Kipi = K2P2 = 1. Use the ideal adsorbed-solution theory to determine ni and n. Substituting the pure component Langmuir isotherm... 

Example 5 Application of Ideal Adsorbed-Solution Theory... 

Freundlich-Type Relations A binary Freundlich isotherm, obtained from the ideal adsorbed solution theory in loading-explicit closed form [Crittenden et al., Environ. Sti. TechnoL, 19,1037 (1985)], is... 

Heterogeneous combustion, 7 449-454 Heterogeneous copolymerization of acrylonitrile, 11 203—204 with VDC, 25 698-699 Heterogeneous enzyme systems, 10 255-256 Heterogeneous gas-solid catalytic reactions, 21 340-341 Heterogeneous Ideal Adsorbed Solution Theory (HIAST), gas separation under, 1 628, 629... 

Idea development, in chemical product design, 5 758, 766-771 Idea generating, in R D, 27 619 Ideal Adsorbed Solution Theory (IAST), 7 594... 

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. 

A mixture equilibria model which is not based on any specific isotherm model does not have the limitations expressed in the derivation of such a model. The Ideal Adsorbed Solution Theory of Jtyers et al. (3 ) is based on the equivalence of the spreading pressures and does not presuppose any isotherm model. In fact, in the original papers, Glessner and Myers (k) stipulated that the model should only be applied using raw equilibrium data to calculate the spreading pressures. This is a very restrictive covenant and does not permit the use of the model for predictive purposes other than that for which data are available. However various authors have applied the Ideal Adsorbed Solution Theory (IAST) model using isotherm models (5., ) quite satisfactorily. 

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 ... 

Heterogeneous Ideal Adsorbed Solution Theory (HIAST). Tliis IAS theory has been extended to the case of adsorbent surface energetic heterogeneity and is shown to provide improved predictions over LAST (12). 

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. 

The ideal adsorbed solution theory of Myers and Prausnitz [13] has been used for developing a multicomponent isotherm model based on the single component isotherm at any pore size. The following result is obtained for the multicomponent isotherm for each component studied in a pore of physical width H (=/f -0.3354)... 

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]. 

The M-S approach allows the prediction of the mixture diffusion based on the pure component M-S diffusivities, along with the mixrnre isotherms (i.e., estimated using the ideal adsorbed solution theory [LAST] of Myers and Prausnitz) [68]. Experimentally, the NMR pulse field gradient technique has been used to calculate the mixture diffusion coefficients. 

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