Spreading pressure multicomponent adsorption

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. 

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 ... 

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 approach of IAS of Myers and Prausnitz presented in Sections 5.3 and 5.4 is widely used to calculate the multicomponent adsorption isotherm for systems not deviated too far from ideality. For binary systems, the treatment of LeVan and Vermeulen presented below provides a useful solution for the adsorbed phase compositions when the pure component isotherms follow either Langmuir equation or Freundlich equation. These expressions are in the form of series, which converges rapidly. These arise as a result of the analytical expression of the spreading pressure in terms of the gaseous partial pressures and the application of the Gibbs isotherm equation. 

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 ... 

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 ... 

---