Multicomponent adsorption theory

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... 

Principles of Adsorption Chromatography The Separation of Nonionic Organic Compounds, Lloyd R. Snyder Multicomponent Chromatography Theory of Interference,... 

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. 

For multicomponent adsorption the most commonly used isotherm is the extended Langmuir isotherm (Eq. 18). Another, frequently used approach is the Ideal Adsorption Solution theory (IAS theory), which was developed by Prausnitz [53] and applied to mixtures of gases by, for example, Kaul [54] and Rees [52,55]. 

H. Habuka, M. Shimada, and K. Okuyama, Rate theory of multicomponent adsorption of organic species on silicon wafer surface, J. Electrochem. Soc. 147, 2319, 2000. 

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

The adsorption of gas mixtures has been extensively studied. For example, Wendland et al. [64] applied the Bom—Green—Yvon approach using a coarse grained density to study the adsorption of subcritical Lennard-Jones fluids. In a subsequent paper, they tested their equations with simulated adsorption isotherms of several model mixtures [65]. They compared the adsorption of model gases with an equal molecular size but different adsorption potentials. They discussed the stmcture of the adsorbed phase, adsorption isotherms, and selectivity curves. Based on the vacancy solution theory [66], Nguyen and Do [67] developed a new technique for predicting the multicomponent adsorption equihbria of supercritical fluids in microporous carbons. They concluded that the degree of adsorption enhancement, due to the proximity of the pore... 

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. 

The theory of the adsorbed solution is a very effective and widely used tool to predict multicomponent adsorption equilibria based on isotherms of single components in the state of gases or vapors. In Table 2.4-4 various submodels of this theory can be found characterizing different adsorbate properties and / or different surface properties of the adsorbent (homogeneous, heterogeneous). 

Table 2.4-4 Adsorbed solution theories for the description or prediction of multicomponent adsorption equilibria. In the light gray area new theoretical models are listed. The theories in the double-framed area require experimental data of binary adsorptives. VLE denotes vapor liquid equilibrium. The meaning of VAE is vapor adsorbate equilibrium...

The FAST-IAST theory introduced by O Brian and Myers (1985) and Moon and Tien (1987) provides a much faster way to calculate multicomponent adsorption equilibria based on the lAST method. The application of the FAST-IAST theory reqirires the determination of the spreading pressme analytically. Next the equations of lAST are remodeled in such a way that a linear system of eqirations is obtained. A gas mixture of N corrrponents which is in equilibrirrm with the adsorbate on the adsorbent has (iV+ 1) degrees of freedom and can be described by (A+ 1) independent variables. These variables are the terrrperature, the pressme, and (N-l) mole fractions of the gas. The N equations for N unknowns can be solved for a given constant temperature. (A/ - 1) equations are obtained by setting equal all reduced spreading pressirres ... 

Moon, H. Tien, C. Further Woik on Multicomponent Adsorption Equihbria Calculations based on the Ideal Adsoibed Solution Theory, Ind. Chem Res. 26 (1987), p. 2042... 

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. 

The last three chapters deal with the fundamental and empirical approaches of adsorption isotherm for pure components. They provide the foundation for the investigation of adsorption systems. Most, if not all, adsorption systems usually involve more than one component, and therefore adsorption equilibria involving competition between molecules of different type is needed for the understanding of the system as well as for the design purposes. In this chapter, we will discuss adsorption equilibria for multicomponent system, and we start with the simplest theory for describing multicomponent equilibria, the extended Langmuir isotherm equation. This is then followed by a very popularly used IAS theory. Since this theory is based on the solution thermodynamics, it is independent of the actual model of adsorption. Various versions of the IAS theory are presented, starting with the Myers and Prausnitz theory, followed by the LeVan and Vermeulen approach for binary systems, and then other versions, such as the Fast IAS theory which is developed to speed up the computation. Other multicomponent equilibria theories, such as the Real Adsorption Solution Theory (RAST), the Nitta et al. s theory, the potential theory, etc. are also discussed in this chapter. 

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. 

In this section, we apply the IAS theory to calculate the multicomponent adsorption equilibria using only pure component data. The data are taken from Szepesy and Hies (1963). 

The IAS theory is a convenient tool to calculate the multicomponent adsorption equilibria, but its predictability is limited, which is mainly due to the assumption of treating the adsorbed phase as one thermodynamic entity. It is this reason that the IAS theory can not predict the azeotropic behaviour commonly encountered in practice, especially systems involving hydrocarbons and carbon oxides in zeolitic adsorbents. One simple way of treating the azeotropic behaviour is to treat the adsorbed phase as a combination of two indendent different adsorbed phases,and the LAS is applied each adsorbed phase. We demonstrate this concept in the following example. 

The ideal adsorption solution theory presented in previous sections provides a useful means to determine the multicomponent adsorption equilibria. The procedure is simple and the method of calculation is also straight forward. The method, unfortunately, only works well when the adsorption systems do not behave too far from ideality. For example, adsorption of the same paraffin hydrocarbon gases on activated carbon can be described well by the IAS theory. However for systems... 

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 ... 

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,... 

Various efforts have also been made to extend the DA equation for the study of the adsorption equilibria of gas/vapor mixtures. The models for multicomponent adsorption equilibria based on the DA equation can be roughly classified into three groups (1) the direct extension or application of the DA (or DR) equation (2) the potential theory approach, which is based on coalescing the potential curves of different components (3) other methods, which link the DA equation to other adsorption properties, such as the adsorbed phase properties or adsorbate-pore interaction potentials. 

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. 

A key concept in the equilibrium theory of multicomponent adsorption is the concept of coherence. Coherent behavior was assumed by most of the early workers, including Glueckauf, but the nature of this assumption appears to have been recognized only more recently by Helfferich. For a dilute equilibrium plug flow system the differential fluid phase mass balance [Eq. (9.1) may be written for each component in the form... 

The importance of heat effects in adsorption column dynamics appears first to have been recognized by Leavitt in the early 1960s but detailed analysis came only some years later. The equilibrium theory of an adiabatic adsorption column, which is closely related to the equilibrium theory of multicomponent adsorption, was first developed by Amundson, Aris, and Swanson and the analysis was extended by Pan and Basmadjian ° who also verified some aspects of the theory in an experimental study of the adsorption of COj and 5A molecular sieve. These initial developments were expanded into a more complete treatment by Rhee, Amundson, and Heerdt as well as in later... 

Tien, C., Incorporation of IAS theory in multicomponent adsorption calculations, Chem. Eng. Commun., 40. 265-280(1986). 

Gamba, G., et al.. Adsorbed solution theory models for multicomponent adsorption equilibria, AIChE J., 35(6). 959-966(1989). 

Gusev, V., et al.. Theory for multicomponent adsorption equilibrium Multispace adsorption model, AIChE J., 42(10), 2773-2783 (1996). 

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