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

Abstract

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.

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

“…After canceling the common P terms and simplifying, eq 34 becomes a second-order expression in P , i.e., where and with its discriminant given by Again, all the possible cases of intersecting and nonintersecting single-gas isotherms resulting from eq 35 are depicted elsewhere. 39 As previously noted with the general DPL model, nonintersecting single-gas isotherms are granted only when both a g > 0 and Δ g < 0, and that it is not possible to have nonintersecting single-gas isotherms when a g < 0. These important conditions are revisited later in this work.…”

“…To prove the notion above, the thermodynamically consistent DPL model was used first because intersecting single-gas isotherms ensure that the corresponding binary gas mixture exhibits an adsorption azeotrope . Several sets of thermodynamically consistent DPL model parameters were found that prove adsorption azeotropes in binary gas mixtures can form at pressures above or below the intersection P of the corresponding single-gas isotherms.…”

“…All of the cases are demonstrated with examples, where the single-gas isotherm parameters are determined by trial and error while using the established constraints from the theoretical developments for each DPL model, just like in the previous work. 39 The results from all 10 cases are displayed in Figures 1 – 5 , with the corresponding single-gas isotherm parameters and adsorption azeotrope existence parameters listed in Table 1 .…”

“…All the possible cases of intersecting and nonintersecting single-gas isotherms resulting from eq 18 are depicted elsewhere. 39 It suffices to state here that nonintersecting single-gas isotherms are granted only when both a f > 0 and Δ f < 0 and that it is not possible to have nonintersecting single-gas isotherms when a f < 0. These conditions are revisited later in this work.…”

“…Therefore, to provide resolution to this puzzling question, the objective of this work is to confirm theoretically whether adsorption azeotropes can form in a binary mixture below the intersection P of the corresponding single-gas isotherms. Like in the previous work by the authors, 39 which showed that an adsorption azeotrope may form in a binary gas mixture when this mixture exhibits nonintersecting or may not form when exhibiting intersecting single-gas isotherms, the thermodynamically consistent and general dual-process Langmuir (DPL) models are used for this purpose. Relationships derived from both DPL models, in terms of the single-gas isotherm DPL model parameters, are used to find examples that disclose the P region in a binary gas mixture where adsorption azeotropes always exist relative to the intersection P of the single-gas isotherms.…”