Modified van der Waals Equation for the Prediction of Multicomponent Isotherms

Theoretical Analysis of the Pressure Regions Where Adsorption Azeotropes Exist in Binary Gas Mixtures

This work confirmed theoretically whether adsorption azeotropes can form in a binary gas mixture at a pressure P below the intersection pressure of the corresponding single-gas isotherms. The thermodynamically consistent dual-process Langmuir (DPL) model with equal component i saturation capacities q _i, j ^s on site j and the general DPL model with nonequal q _i, j ^s on site j were used for this purpose. Relationships derived from both DPL models, in terms of the single-gas isotherm DPL model parameters, were used to answer this question. When the P range where adsorption azeotropes always exist is infinite beyond the onset P of adsorption azeotropic formation, both DPL models and experimental data showed that it is possible to form adsorption azeotropes in the corresponding binary gas mixture at pressures not only above but even below the single-gas isotherm intersection P. When the P range where adsorption azeotropes always exist is finite beyond the onset P of adsorption azeotropic formation, only the general DPL model predicts the onset P of this finite P range can be below the intersection P of the corresponding single-gas isotherms. Without theoretical proof, the thermodynamically consistent DPL model seemingly restricts this P range to be equal to or greater than the intersection P of the corresponding single-gas isotherms. For a finite P region where adsorption azeotropes always exist in a binary gas mixture, the binary selectivity inverts when traversing from below the lower onset P to the higher cessation P. Both models also showed, counterintuitively, that perfect positive energetic site matching can result in the formation of adsorption azeotropes in binary gas mixtures, not just perfect negative energetic site matching. Overall, this work provides some confirmation that it is indeed possible to form adsorption azeotropes in a binary gas mixture at pressures below the intersection P of the corresponding single-gas isotherms based on two physically sound formulations of the DPL model.

Theoretical Analysis of the Necessary and Sufficient Conditions for the Formation of Adsorption Azeotropes in Binary Gas Mixtures

This work theoretically assessed the necessary and sufficient conditions for the formation of an adsorption azeotrope in a binary gas mixture when this mixture exhibits either intersecting or nonintersecting single gas isotherms. The thermodynamically consistent dual process Langmuir (DPL) model with equal component i saturation capacities q_i,j^s on site j and the general DPL model with nonequal q_i,j^s on site j were used for this purpose. Analytical expressions derived for both DPL models, in terms of the single gas isotherm DPL model parameters, were used to find examples or to determine theoretically when an adsorption azeotrope forms in a binary gas mixture for both intersecting and nonintersecting single gas isotherms. For the general DPL model, it was determined that neither necessary nor sufficient conditions exist for the formation of an adsorption azeotrope in a binary gas mixture. This means that an adsorption azeotrope can form irrespective of whether the corresponding single gas isotherms intersect or not. For the thermodynamically consistent DPL model, it was determined that the intersection of the single gas isotherms is a sufficient condition for the formation of an adsorption azeotrope in a binary gas mixture, but it is not a necessary condition. This means that intersecting single gas isotherms guarantee the formation of an adsorption azeotrope in the corresponding binary gas mixture, while nonintersecting single gas isotherms can also result in the formation of an adsorption azeotrope in the corresponding binary gas mixture. Overall, this analysis provides a well-posed resolution to the question of necessity and sufficiency for the formation of adsorption azeotropes in binary gas mixtures and the intersection of their corresponding single gas isotherms based on two physically sound formulations of the very popular DPL model.

Modeling of Gas Adsorption Equilibrium over a Wide Range of Pressure: A Thermodynamic Approach Based on Equation of State

A thermodynamic approach based on the Bender equation of state is suggested for the analysis of supercritical gas adsorption on activated carbons at high pressure. The approach accounts for the equality of the chemical potential in the adsorbed phase and that in the corresponding bulk phase and the distribution of elements of the adsorption volume (EAV) over the potential energy for gas-solid interaction. This scheme is extended to subcritical fluid adsorption and takes into account the phase transition in EAV. The method is adapted to gravimetric measurements of mass excess adsorption and has been applied to the adsorption of argon, nitrogen, methane, ethane, carbon dioxide, and helium on activated carbon Norit R1 in the temperature range from 25 to 70 degrees C. The distribution function of adsorption volume elements over potentials exhibits overlapping peaks and is consistently reproduced for different gases. It was found that the distribution function changes weakly with temperature, which was confirmed by its comparison with the distribution function obtained by the same method using nitrogen adsorption isotherm at 77 K. It was shown that parameters such as pore volume and skeleton density can be determined directly from adsorption measurements, while the conventional approach of helium expansion at room temperature can lead to erroneous results due to the adsorption of helium in small pores of activated carbon. The approach is a convenient tool for analysis and correlation of excess adsorption isotherms over a wide range of pressure and temperature. This approach can be readily extended to the analysis of multicomponent adsorption systems.