Prediction of Multicomponent Adsorption Equilibria

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). 

The basis of all models is the ideal adsorption solution theory (lAST) published by Myers and Prausnitz (Myers and Prausnitz 1965). The basic assumption is the equality of the chemical potential of the component / in the gas phase 

In these equations, p T) is the chemical standard potential of the component i, p is a standard pressure, tt is the spreading pressure of the adsoibed solution, and /i is an activity coefficient. The virtual pressure p ( ) (not the vapor pressure) depends on the spreading pressure and is the pressure of the component / which has the same spreading pressure either in the pure state or in the gaseous mixture. The equality q = g in the case of thermodynamic equilibrium leads to Raoult s law of adsorption 

Adsorbed solution theories Energy distribution of the adsorbent surface  

Ideal adsorbed solution Activity coefficient / = 1 Ideal adsorbed solution theory (lAST) Multiphase ideal adsorbed solution theory (MIAST) Heterogeneous ideal adsorbed solution theory (HIAST) 

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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. 

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. 

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...

Table 5 shows examples of LDF mass transfer coefficients for adsorption of several binary gas mixtures on BPL activated carbon particles (6-16 mesh) at 23-30°C. The data show that the mass transfer coefficients are relatively large for these systems. There is a scarcity of multicomponent adsorption equilibria, kinetics, and heat data in the published literature. This often restricts extensive testing of theoretical models for prediction of multicomponent behavior. 

Adsorption measurement for multicomponent systems is a function of the composition, temperature, pressure, and properties of adsorbate and adsorbent. As the number of components increases, the number of measurements needed to define the adsorption equilibrium increases rapidly and eventually becomes infeasible. Adsorption equilibrium models are therefore needed to correlate and predict the multicomponent adsorption equilibria. These models should be able to predict the mixture equilibria using the information available on pure component equilibria, as the latter are relatively easy to measure and furthermore there is an abundance of pure component isotherm data available in the literature. As a result, predictive models for gas mixture adsorption are necessary in the design and modeling of adsorption processes. 

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,... 

It can be seen that lAST predictions seriously deviate from the experimental data for this system even though the adsorbed phase is known to be very close to ideal under the experimental conditions. This deviation therefore points to the surface heterogeneity. T o address this heterogeneity, new models continue to emerge in the study of multicomponent adsorption equilibria. 

Multicomponent pollutants in an aqueous environment and/or leachate of SWMs, which are COMs, usually consist of more than one pollutant in the exposed environment [1, 66-70]. Multicomponent adsorption involves competition among pollutants to occupy the limited adsorbent surface available and the interactions between different adsorbates. A number of models have been developed to predict multicomponent adsorption equilibria using data from SCS adsorption isotherms. For simple systems considerable success has been achieved but there is still no established method with universal proven applicability, and this problem remains as one of the more challenging obstacles to the development of improved methods of process design [34,71 - 76]. 

They have been found useful as an empirical correlation method for adsorption on molecular sieves [Maurer, Am. Chem. Soc. Symp. Ser. 135, 73 (1980)]. Other attempts at prediction or correlation of multicomponent adsorption data are reviewed by Ruthven (1984). In general, however, multicomponent equilibria are not well correlatable in general form so that design of equipment is best based on direct laboratory data with the exact mixture and the exact adsorbent at anticipated pressure and temperature. 

Ideal Adsorbed Solution Theory. Perhaps the most successful general approach to the prediction of multicomponent equilibria from single-component isotherm data is ideal adsorbed solution theory. In essence, the theory is based on the assumption that the adsorbed phase is thermodynamically ideal in the sense that the equilibrium pressure for each component is simply the product of its mole fraction in the adsorbed phase and the equilibrium pressure for the pure component at Ike same spreading pressure. 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. 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, are not consistent with an ideal adsorbed phase and there is no way of knowing a priori whether or not a given system will show ideal behavior. 

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 ... 

To study the influence of the pore network connectivity on multicomponent adsorption equilibria, we used ethyl propionate, ethyl butyrate, and ethyl isovalerate as the adsorbates and Filtrasorb-400 and Norit ROW 0.8 activated carbon as the adsorbents. For predicting binary isotherms we used known parameters for single component adsorption of these compounds as previously determined. The effect of the pore network connectivity was taken into account in... 

Generally, wastewaters are complex mixtures of solutes, which require theoretical approaches to predict multicomponent adsorption equilibria flxtm pure component adsorption data. The Ideal Adsorbed Solution model (IAS) was first established for a mixed gas adsorption by Myers and Prausnitz [9], and then extended to a multi-solute adsorption from dilute liquid solution by Radke and Prausnitz [10]. The model is based on the fundamental hypothesis that the multicomponent solution has the same spreading pressure s as that of the ideal single solution of the i component, the spreading pressure being the difference between the interfacial tension of the pure solvent and that of the solution containing the solute. This hypothesis is described by the Gibbs equation ... 

The prediction of multicomponent equilibria based on the information derived from the analysis of single component adsorption data is an important issue particularly in the domain of liquid chromatography. To solve the general adsorption isotherm, Equation (27.2), Quinones et al. [156] have proposed an extension of the Jovanovic-Freundlich isotherm for each component of the mixture as local adsorption isotherms. They tested the model with experimental data on the system 2-phenylethanol and 3-phenylpropanol mixtures adsorbed on silica. The experimental data was published elsewhere [157]. The local isotherm employed to solve Equation (27.2) includes lateral interactions, which means a step forward with respect to, that is, Langmuir equation. The results obtained account better for competitive data. One drawback of the model concerns the computational time needed to invert Equation (27.2) nevertheless the authors proposed a method to minimize it. The success of this model compared to other resides in that it takes into account the two main sources of nonideal behavior surface heterogeneity and adsorbate-adsorbate interactions. The authors pointed out that there is some degree of thermodynamic inconsistency in this and other models based on similar -assumptions. These inconsistencies could arise from the simplihcations included in their derivation and the main one is related to the monolayer capacity of each component [156]. 

When binary activity coefficients can only be obtained from experimental equilibrium data, there is no way to predict multicomponent adsorption equiUbria which are only based on single component isotherms however, such a procedure would be desirable. The SPDM (spreading pressure dependent model) contains only predictive parameters with the exception of the binary parameter (Markmarm 1999 Mersmann et al. 2002). Setting p j = 0, this method allows to calculate multicomponent adsorption equilibria without experimental data obtained for binary mixtures. 

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 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. 

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. 

Occasionally, isotherms of binary and multicomponent exchanges are described using various empirical adsorption equations. These cannot be used for the prediction of multicomponent equilibria [88]. In fact, a closer inspection of these equations reveals that they have no in-built facility for true prediction (i.e. for the calculation of equilibria over ranges of different total solution concentrations for heterovalent exchanges). Thus these equations are useful in describing the observed isotherm in a mathematical form but the only pre-... 

The Langmuir model for competitive adsorption can be used as a common model for predicting adsorption equilibria in multicomponent systems. This was first developed by Butler and Ockrent [77] and is based on the same assumptions as the Langmuir model for single adsorbates. It assumes, as in the case of the Langmuir model, that the rate of adsorption of a species at equilibrium is equal to its desorption rate. This is expressed by Eq. (18) ... 

All cases of practical importance in liquid chromatography deal with the separation of multicomponent feed mixtures. As shown in Chapter 2, the combination of the mass balance equations for the components of the feed, their isotherm equations, and a chromatography model that accounts for the kinetics of mass transfer between the two phases of the system permits the calculation of the individual band profiles of these compounds. To address this problem, we need first to understand, measure, and model the equilibrium isotherms of multicomponent mixtures. These equilibria are more complex than single-component ones, due to the competition between the different components for interaction with the stationary phase, a phenomenon that is imderstood but not yet predictable. We observe that the adsorption isotherms of the different compounds that are simultaneously present in a solution are almost always neither linear nor independent. In a finite-concentration solution, the amount of a component adsorbed at equilib-... 

Information concerning the relevant adsorption equilibria is generally an essential requirement for the analysis and design of an adsorption separation process. In Chapter 3 we considered adsorption equilibrium from the thermodynamic perspective and developed a number of simple idealized expressions for the equilibrium isotherm based on various assumptions concerning the nature of the adsorbed phase. The extent to which these models can provide a useful representation of the behavior of real systems was considered only superficially and is reviewed in this chapter. Since many practical adsorption systems involve the simultaneous adsorption of more than one component, the problems of correlating and predicting multicomponent equilibria from singlecomponent data are of particular importance and are therefore considered in some detail. 

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