An explicit multicomponent adsorption isotherm model: accounting for the size-effect for components with Langmuir adsorption behavior

Abstract: The extended Langmuir (EL) model is a popular multicomponent adsorption equilibria model, which can be based on single component Langmuir isotherms fitted on pure component data. Such explicit models are preferred over their implicit counterparts due to a lower computational requirement. An important shortcoming of the EL model is its inability to capture the adsorbate size effect occurring when the saturation capacities of pure component Langmuir isotherms are dissimilar. In contrast, this size effect is captured by the ideal adsorbed solution theory (IAST), which is centered on a set of implicit equations. In this work, we present an explicit multicomponent adsorption model for components with uneven saturation capacities obeying the Langmuir isotherm equation. This model predicts the expected change in selectivity with mixture composition, and even a selectivity reversal at high pressure when the adsorbates have significantly different molecular sizes. The model is extendable to any number of components, reduces to the Langmuir equation for pure components and to the EL equation when all saturation capacities are equal. The newly proposed model can be used to approximate the IAST and upgrade the EL model without introducing new parameters. Especially for binary mixtures, this model (Eqs. 12–14) offers a simple improvement of the EL model in predicting the experimental adsorption of light alkanes on 13X and 5A zeolites. The presented model is also applied to describe phase-changing adsorbents, in combination with the osmotic framework adsorbed solution theory (OFAST).