Multicomponent adsorption ideal adsorbed solution theories

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... 

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. 

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. 

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. 

Crittenden, J.C., Luft, P.J., Hand, D.W., et al. (1985). Prediction of multicomponent adsorption equifibiia using ideal adsorbed solution theory. Environ. Sci. TechnoL, 19(11), 1037-43. 

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,... 

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 ... 

In many cases, the surface phase may be assumed to be ideal and its activity coefficients f set unity. The corresponding theory has been called lAST (Ideal Adsorbed Solution Theory) [80]. The main advantage of the lAST is its capabdity to predict multicomponent adsorption equilibria on the basis of the experimental data on the single-component adsorption. Relations (43) and (44) are greatly simplified in this case. 

Although the role of solvent has been discussed qualitatively, our discussion in this chapter has been limited to single adsorption (one solute-one surface). Multicomponent adsorption is a much more complex subject and many theories have been proposed, e.g. an extension of the Langmuir theory and different approaches like the ideal adsorbed solution theory (lAST) and the multicomponent potential adsorption theory (MPTA). They will be discussed in Chapter 14. 

Myers and Prausnitz [49] developed the ideal adsorbed solution (IAS) model in order to predict thermodjmamically consistent multicomponent isotherms of gas mixtures, using only experimental data acquired for single solute adsorption. The initial equation of the IAS theory for gases is... 

Engineering theories for multicomponent adsorption can be roughly divided into three categories extensions of the Langmuir equation, the thermodynamic approach (ideal and real adsorbed solution theories, lAST and RAST) by Myers and Prausnitz (1965) and finally the potential adsorption theory, especially as extended to multi-component systems by Shapiro and co-workers (Shapiro and Stenby, 1998 Monsalvo and Shapiro, 2007a, 2009a,b). 

Three theories for multicomponent adsorption have been presented, the extension of Langmuir s theory to multicomponent systems, the ideal and real adsorbed solution theories (lAST, RAST) and the multicomponent potential adsorption theory (MPTA). 

Chapters 2 to 4 deal with pure component adsorption equilibria. Chapter 5 will deal with multicomponent adsorption equilibria. Like Chapter 2 for pure component systems, we start this chapter with the now classical theory of Langmuir for multicomponent systems. This extended Langmuir equation applies only to ideal solids, and therefore in general fails to describe experimental data. To account for this deficiency, the Ideal Adsorption Solution Theory (lAST) put forward by Myers and Prausnitz is one of the practical approaches, and is presented in some details in Chapter 5. Because of the reasonable success of the IAS, various versions have been proposed, such as the FastlAS theory and the Real Adsorption Solution Theory (RAST), the latter of which accounts for the non-ideality of the adsorbed phase. Application of the RAST is still very limited because of the uncertainty in the calculation of activity coefficients of the adsorbed phase. There are other factors such as the geometrical heterogeneity other than the adsorbed phase nonideality that cause the deviation of the IAS theory from experimental data. This is the area which requires more research. 

For multicomponent systems obeying the ideal adsorption solution theory, the spreading pressure of the adsorbed mixture is n. The partial pressure of the species i in the gas phase is related to the hypothetical pure component pressure which gives the same spreading pressure n as that of the mixture according to the Raoult s law analogy ... 

The vacancy solution theory was developed by Suwanayuen and DanneE as a method of predicting multicomponent adsorption equilibria from singlecomponent isotherms without the assumption of an ideal adsorbed phase. A somewhat different analysis is given here although the essential features of the model are retained. 

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