Model ideal adsorbed solution

FIGURE 4.22. X- F diagram for adsorption of isobulane-elhyleiie on I3X sieve at 50 C, 20 psi (absolute), showing comparison of predictions from statistical model ideal adsorbed solution... 

The potential model has been applied to the adsorption of mixtures of gases. In the ideal adsorbed solution model, the adsorbed layer is treated as a simple solution, but with potential parameters assigned to each component (see Refs. 76-79). 

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. 

Ideal Adsorbed Solution (IAS) Model For components i andassuming ideal gas behavior, this model (36) is... 

The most common model for describing adsorption equilibrium in multi-component systems is the Ideal Adsorbed Solution (IAS) model, which was originally developed by Radke and Prausnitz [94]. This model relies on the assumption that the adsorbed phase forms an ideal solution and hence the name IAS model has been adopted. The following is a summary of the main equations and assumptions of this model (Eqs. 22-29). 

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 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... 

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]. 

As has become clear adsorption phenomena play an important, if not, decisive role in this behaviour, and good data and modelling of adsorption are mandatory, too, to serve as the input parameters for the permeation description. This should not be l ted to the T.angmnir model, but other theories like the IAS (ideal adsorbed solution) and NIAS (non-ideal) should be considered, since they sometines work well for binary systems where the Langmuir model fails. 

As a forerunner to the landmark publications of Muller and coworkers [523-525], Jossens et al. [678] presented an ideal-adsorbed-,solution (IAS) model for... 

Unfortunately, the available experimental results suggest that the column saturation capacity is often not the same for the components of a binary mixture, so Eq. 4.5 does not account accurately for the competitive adsorption behavior of these components [48]. A simple approach was proposed to turn the difficulty (next subsection). Although it is applicable in some cases, more sophisticated models seem necessary. Numerous isotherm models have been suggested to solve this problem. Those resulting from the ideal adsorbed solution (IAS) theory developed by Myers and Prausnitz [49] are among the most accurate and versatile of them. Later, this theory was refined to accormt for the dependence of the activity coefficients of solutes in solution on their concentrations, leading to the real adsorption solution (RAS) theory. In most cases, however, the equations resulting from IAS and the RAS theories must be solved iteratively, which makes it inconvenient to incorporate those equations into the numerical calculations of column dynamics and in the prediction of elution band profiles. 

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... 

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. 

The fifth approach is more a field than a concise method, since it embodies so many theoretical concepts and associated methods. All are grouped together as adsorbed mixture models. Basically, this involves treating the adsorbed mixture in the same manner that the liquid is treated when doing VLE calculations. The major distinction is that the adsorbed phase composition cannot be directly measnred (i.e., it can only be inferred) hence, it is difficult to pursue experimentally. A mixture model is nsed to account for interactions, which may be as simple as Raoult s law or as involved as Wilson s equation. These correspond roughly to the Ideal Adsorbed Solution theory and Vacancy Solution model, respectively. Pure component and mixture equilibrium data are required. The unfortunate aspect is that they require iterative root-finding procedures and integration, which complicates adsorber simnlation. They may be the only route to acceptably accurate answers, however. It would be nice if adsorbents could be selected to avoid both aspects, but adsorbate-adsorbate interactions may be nearly as important and as complicated as adsorbate-adsorbent interactions. 

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 ... 

In contrast to the binary Langmuir or SSTM models, the ideal adsorbed solution theory does not lead to a simple explicit relation for the adsorbed-phase composition and loading in terms of the partial pressures. Calculation of the equilibrium for a particular gas-phase composition therefore requires a trial and error procedure. 

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. 

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. 

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. 

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