(381g) Generalized Langmuir (gL) Isotherm for Mixed-Gas Adsorption Equilibria on MFI and LTA Adsorbents

Driven by the need to replace energy-intensive thermal separation with energy-efficient and sustainable separation technologies, adsorption has garnered immense interest and significant advancements have been made in both the development of novel adsorbents and the understanding and modeling of adsorption behavior in recent years¹. To support simulation, design, and optimization of adsorption processes for various applications, the ability to accurately predict adsorption behavior of gas mixtures with rigorous thermodynamic models is essential.

Thus far, there are two distinct and commonly practiced thermodynamic frameworks for mixed-gas adsorption equilibria. First, the extended Langmuir Isotherm² and its dual site variation, i.e., Dual Process Langmuir isotherm, are empirical extensions of the classical Langmuir isotherm and often faulted with thermodynamic inconsistency and over-parameterization. Second, Ideal/Real Adsorbed Solution Theory (IAST/RAST)³ removes adsorbent sites from the thermodynamic consideration, introduces an extra state variable called “spreading pressure” to track the surface loading, and treats mixed-gas adsorption equilibria with Raoult's Law in vapor-liquid equilibria. While IAST/RAST is thermodynamically consistent and considered to be the benchmark thermodynamic framework for adsorption equilibria, it offers 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 has emerged for mixed-gas adsorption equilibria. Named generalized Langmuir (gL) isotherm⁴, this new isotherm considers the competitive adsorption of multiple adsorbates on a constant adsorbent surface area, treats adsorption sites 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. 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 both the CO₂-CH₄-C₂H₄ system on MFI and the CO₂-CH₄-C₃H₆ system on LTA adsorbent over a range of temperature (293, 303, and 313 K) and pressure (0.01 to 10 bar for MFI and 0.00001 to 10 bar for LTA,). The results show the gL isotherm is a robust and practical adsorption thermodynamic model for mixed-gas adsorption equilibria.

References:

1. Mozaffari Majd, M., Kordzadeh-Kermani, V., Ghalandari, V., Askari, A., and Sillanpää, M., 2022. Adsorption isotherm models: A comprehensive and systematic review (2010−2020). Science of the Total Environment, 812, p. 151334.
2. Kapoor, A., Ritter, J. A., and Yang, R.T., 1990. An extended Langmuir model for adsorption of gas-mixtures on heterogeneous surfaces. Langmuir, 6, p.660664.
3. Myers, A. L., and Prausnitz, J. M., 1965. Thermodynamics of Mixed-Gas Adsorption. AIChE Journal, 11, p. 121127.
4. Hamid, U., Vyawahare, P., Tun, H., and Chen, CC., 2021. Generalization of thermodynamic Langmuir isotherm for mixed-gas adsorption equilibria. AIChE Journal, 68, p. e17663.
5. Kaur, H., Tun, H., Sees, M., and Chen, CC., 2019. Local composition activity coefficient model for mixed‑gas adsorption equilibria. Adsorption, 25, p. 951964.