Thus far, there are two distinct and commonly practiced thermodynamic frameworks for mixed-gas adsorption equilibria. First, the extended Langmuir Isotherm model2 and its dual site variation, i.e., Dual Process Langmuir isotherm model, are empirical extensions of the classical Langmuir isotherm model and often faulted with thermodynamic inconsistency and over-parameterization. Second, the Ideal/Real Adsorbed Solution Theory (IAST/RAST) models3 remove adsorbent sites from the thermodynamic consideration, introduce an extra state variable called “spreading pressure” to track the surface loading, and treat mixed-gas adsorption equilibria with Raoult's Law in vapor-liquid equilibria. While IAST/RAST models are thermodynamically consistent and considered to be the benchmark thermodynamic framework for mixed-gas adsorption equilibria, they offer no physical insight for mixed-gas adsorption behavior, and it is computationally intensive due to the need to search and satisfy the "spreading pressure" constraint. Recently, a thermodynamically consistent extension of the classical Langmuir isotherm model has emerged for mixed-gas adsorption equilibria. Named generalized Langmuir (gL) isotherm model4, it considers the competitive adsorption of multiple adsorbates on a constant adsorbent surface area, treats adsorption sites explicitly as part of the thermodynamic system, substitutes species concentrations with activities, considers surface heterogeneity, adsorbent-adsorbate interactions, and adsorbate-adsorbate interactions with an adsorption NRTL5 activity coefficient model. A significant limitation of the adsorption NRTL model is its inability to account for the entropy contribution due to adsorbate size effect, which arises when the surface loading approaches saturation for mixed-gas adsorbates with different sizes.
The current study examines and compares the model performance of gL and IAST/RAST based on the molecular simulation-generated data for the pure component isotherms, isosteric heat of adsorption, and binary and ternary mixed-gas adsorption equilibrium for the CO2-CH4-C3H6 system on LTA adsorbent over a range of temperature (293, 303, and 313 K) and pressure (0.00001 to 10 bar). The results show that although the gL isotherm is a robust and practical thermodynamic model for mixed-gas adsorption equilibria, an improvement of the gL model is needed for adsorption systems under high pressure and high loading conditions by improving the adsorbed phase activity coefficient model with the entropy contribution. This new gL model predicts the selectivity reversal at high loadings for adsorption systems with adsorbates exhibiting significant differences in molecular size, as observed for this CO2-CH4-C3H6 system on LTA adsorbent.
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