Analytical and numerical estimations of isosteric heat of adsorption with application to hydrogen purification

The isosteric heat of adsorption or isosteric enthalpy of adsorption represents a crucial thermodynamic parameter facilitating the assessment and improvement of adsorption processes. This study comprehensively summarizes the analytical and numerical multi-estimations of the isosteric heat of adsorption using the Clausius-Clapeyron equation based on the commonly used adsorption isotherm models. The widely-used dual-site Langmuir-Freundlich (DSLF) model, adept at characterizing multiple adsorption energy sites and heterogeneous surfaces of porous materials, serves as the foundation for deriving a general analytical expression for the isosteric heat. The general analytical expression derived based on the DSLF model proves effective across a spectrum of models, including the dual-site Langmuir (DSL), single-site Langmuir-Freundlich (SSLF), single-site Langmuir (SSL), Freundlich and Henry’s law isotherm models. Leveraging the general analytical expression, a user-friendly GUI calculator was developed to facilitate swift calculation of the isosteric heat of adsorption. A detailed comparison of the analytical and numerical estimations of the isosteric heat for the commonly used adsorption isotherm models is performed. The results revealed that the analytical and numerical results for isosteric heats obtained from different adsorption isotherm models were nearly identical. The findings underscore the substantial influence of different adsorption isotherm models on the isosteric heat of adsorption, emphasizing the significance of selecting the appropriate model contingent upon the adsorbent and adsorbate type. In practical applications, the analytical expression of isosteric adsorption heat proves to be more applicable, leading to improved breakthrough curves and temperature profiles of a four-component hydrogen mixture (H₂/CH₄/CO/CO₂) in the pressure swing adsorption (PSA) process for hydrogen purification compared to using the average heat of adsorption.