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Comparison of Heterogeneous Langmuirian Models for Mixed-Gas Adsorption Equilibria

Mixed-gas adsorption remains a very active area of research, where newly proposed adsorption equilibrium models need to be compared to standards in the field. The generalized Langmuir (gL) isotherm, proposed by Hamid et al. to address adsorption of different size molecules on heterogeneous adsorbents without requiring evaluation of the Gibbs isotherm, has thus far been tested mainly against the adsorbed solution theory (AST). The gL isotherm was shown to be thermodynamically consistent and gave either better or similar representation than AST models. Here, the gL isotherm is contrasted with the Dual-Process Langmuir isotherm popularized by Ritter and his co-workers and the Loading Ratio Correlation popularized for simple mixtures, both of which are considered the “standard” models for process simulation. Furthermore, the comparison is based on their theoretical roots, interpretations, and representation of the equilibrium loading and the isosteric enthalpy of adsorption of unary, binary, and ternary mixtures of various gaseous adsorbates on different adsorbents over a range of experimental pressures and temperatures.

42 ENGINEERING↗

Generalized Brunauer–Emmett–Teller Isotherm for Mixed-Gas Multilayer Adsorption Equilibria

Here, this work presents a rigorous thermodynamic framework to calculate mixed-gas multilayer adsorption equilibria from single-component isotherms and vapor–liquid equilibria. Named the generalized Brunauer–Emmett–Teller (gBET) isotherm, the newly formulated isotherm considers adsorbent surface heterogeneity, competitive adsorption on the monolayer, condensation–evaporation on the subsequent layers, and adsorbed phase nonideality for the monolayer and the subsequent layers. The monolayer adsorbed phase nonideality is tracked by using an area-based adsorption nonrandom two-liquid activity coefficient model. The adsorbed phase composition and corresponding nonideality in the subsequent layers are calculated at the dew point condition of the mixed gas with either an equation of state or an activity coefficient model for the vapor–liquid equilibria. The proposed model is validated with six single and three binary multilayer adsorption equilibrium systems, and the model results are compared against those from the classical BET isotherm for single-component adsorption and ideal adsorbed solution theory for mixed-gas adsorption equilibria.

09 BIOMASS FUELS↗

Estimation of isosteric heat of adsorption from generalized Langmuir isotherm

Simulation and design of adsorptive separation units demand accurate estimation of thermodynamic properties. Isosteric heat of adsorption as calculated from generalized Langmuir (gL) isotherm coupled with Clausius-Clapeyron expression for pure component and mixed-gas adsorption equilibria is presented in this work. The estimated isosteric heat of adsorption as functions of surface loading and composition is validated against the experimental data for various adsorption systems. Furthermore, the gL results are compared against classical Langmuir (cL) and Toth isotherm for pure components and with Ideal Adsorbed Solution Theory (IAST) for mixed-gas adsorption equilibria. Furthermore, the comparison highlights that gL outperforms cL and Toth for pure component adsorption and IAST for mixed-gas adsorption, and gL reliably captures the loading dependence and the composition dependence for isosteric heat of adsorption.

42 ENGINEERING↗

Addressing spreading pressure dependence of real adsorbed solution theory with generalized Langmuir isotherm

This work addresses spreading pressure dependence of Real Adsorbed Solution Theory (RAST) for mixed-gas adsorption equilibria using generalized Langmuir (gL) isotherm. Considering vacant sites as an integral part of competitive multicomponent adsorption on a constant adsorbent surface area, the gL isotherm properly accounts for surface heterogeneity and loading, adsorbate composition, and temperature dependence. We show the spreading pressure dependence of adsorbate activity coefficient expression in the RAST framework can be generated from the gL isotherm. The procedure is illustrated with a spreading pressure dependent adsorption Nonrandom Furthermore, two-Liquid activity coefficient model, and the results are validated for ten binary mixed-gas adsorption equilibria systems including two highly nonideal azeotropic systems.

42 ENGINEERING↗

Thermodynamic modeling of adsorption at the liquid-solid interface

Adsorptive separation techniques are significantly energy efficient in comparison to conventional thermal separation techniques such as distillation. Despite extensive research and development activities undertaken for mixed-gas adsorption, the use of adsorption techniques for the separation of multicomponent liquid mixtures is still limited. A major barrier is the lack of accurate adsorption thermodynamic models, which form the scientific foundation of process simulation of such systems, making the translation to industrial scale challenging. In this work, we have rigorously computed the surface excess of adsorption for six binary liquid mixtures on silica gel at 303 K using the frameworks of the generalized Langmuir isotherm (gL) and the adsorbed solution theory (AST). The six binary liquid mixtures were formed by the pair-wise combinations of four components: benzene, 1,2-dichloroethane, cyclohexane, and n-heptane. We have based our calculations by considering simultaneous equilibria of three phases: saturated vapor phase, bulk liquid phase, and adsorbed phase. Further, the composition of the corresponding saturated vapor phase was estimated by the Nonrandom Two-Liquid activity coefficient model and experimental vapor-liquid equilibria data. The activity coefficients of the adsorbed phase, the central issue of multicomponent adsorption thermodynamics, were calculated using the adsorption Nonrandom Two-Liquid activity coefficient model. Devoid of simplifying assumptions, gL and AST provide rigorous thermodynamic frameworks for adsorption equilibria of multicomponent liquid mixtures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On the Thermodynamic Condition for Adsorption Azeotropes

Adsorption azeotropy is a common phenomenon in mixed-gas adsorption equilibria. Since the first literature report of binary adsorption azeotropes in 1933, numerous studies investigated the thermodynamic conditions for adsorption azeotropes but failed to reach definitive conclusions. Based on the generalized Langmuir isotherm model for multicomponent adsorption equilibria which takes into account the vacant site as part of the adsorbed phase, this study presents the thermodynamic condition for adsorption azeotropes as derived from the generalized Langmuir isotherm to be the equality of the ratios of adsorbed phase activity coefficient γi and adsorption equilibrium constant $K$$^{o}_{i}$ for the two adsorbates in the binary 1–2 adsorption system, i.e., γ 1 /$K$$^{o}_{1}$ = γ 2 /$K$$^{o}_{2}$. This adsorption azeotropic condition is analogous to the vapor–liquid equilibrium azeotropic condition, i.e., the equality of the products of liquid phase activity coefficient and saturation vapor pressure Pisat for the two components, i.e., γ 1 $P$$^{sat}_{1}$ = γ 2 $P$$^{sat}_{2}$. We validated the thermodynamic condition for adsorption azeotropes with 14 azeotrope-forming adsorption systems in this study. As a result, we investigated the effects of the pressure, temperature, and adsorbed phase nonideality on azeotrope formation.

42 ENGINEERING↗

Insights on carbon dioxide adsorption in a flexible 1-D coordination polymer from in situ X-ray scattering and density functional theory

A combination of in situ small-angle X-ray scattering (SAXS) microstructure characterization over scales ranging from 1 nm to 10 µm and powder X-ray diffraction (XRD) structure characterization under various gas/pressure/temperature conditions with density functional theory (DFT) calculations provides new insights for the CO2 sorption behavior of a one-dimensional porous coordination polymer: catena-bis­(di­benzoyl­methanato)(4,4′-bi­pyridyl)­nickel(II), denoted NiDBM-Bpy. The NiDBM-Bpy chains are held together by van der Waals forces, but the structure of guest-free NiDBM-Bpy is unsolved due to a lack of suitable crystals and high-quality powder XRD patterns. Nevertheless, SAXS and powder XRD can follow microstructural and structural changes as a function of gas pressure, composition and temperature. Both mixed-gas flow and static supercritical CO2 regimes are explored experimentally. DFT calculations are used to model the structural variation associated with XRD changes and hysteresis in the sorption isotherms. XRD and DFT calculations suggest that an orthorhombic Fddd structure with two CO2 per Ni emerges following a transition from the structure with lower molar volume and symmetry that exists without CO2 present.

Allen, Andrew J.↗