Vacancy Solution Research Articles

Vacancy solution model using the aNRTL activity coefficient for prediction of binary adsorption equilibria

Based on the Vacancy Solution Model (VSM) and the Adsorption Non-Random Two-Liquid (aNRTL) model of the activity coefficient, a novel model called VSM-aNRTL for gas adsorption equilibria is introduced. In this study, an innovative isotherm equation was applied to experimental monocomponent adsorption equilibrium data from the NIST/ARPA-E Database. The parameters derived from this application were subsequently utilized to predict the equilibrium data for 12 binary adsorption systems across three distinct temperatures, employing the extended model. The proposed model proved effective in correlating the adsorption isotherms of pure components, achieving a reduction in the number of adjustable parameters compared to the original VSM that employs the Wilson activity coefficient. It also outperformed the Ideal Adsorbed Solution Theory (IAST) model by incorporating only one additional parameter. Furthermore, the new model was employed to predict the equilibrium data of binary mixture adsorption, demonstrating results with lower deviations compared to both the IAST and the traditional VSM-Wilson models.

Electron and Mass Transfer during Solid Carbon Reduction of Metals in Solid Complex Oxides

The possibility of iron and chromium reduction in the composition of complex oxides by gaseous carbon monoxide and solid carbon was studied in a laboratory resistance furnace with a graphite heater. Holding only a CO atmosphere does not reduce chromium and iron in both chromites and silicates. In a mixture with solid carbon, chromium and iron were completely reduced in chromites, and iron precipitated in an iron–magnesia silicate matrix in the part having undergone hydration in nature and dehydration upon heating. Continuous carbide shells, which exactly reproduce a surface relief, appear on the surfaces of solid oxide and carbon in a mixture of solid reagents. Similar shells consisting of a carbon-free FeCr alloy form on the surfaces of chromite crystals disseminated in a silicate phase. These results do not correspond to the concepts of both direct and indirect reduction, and they are analyzed in terms of electronic reduction theory developed by us. According to this theory, a low-temperature plasma appears in a mixture of solid reagents due to thermionic electron emission from the carbon surface. As a result, charged particles, namely, electrons and carbon cations, appear near the reagent surfaces. Their interaction with oxide anions causes the formation of CO and anion vacancies, which are charged by two electrons and are scattered in the anion sublattice of oxide. The saturated vacancy solution in the anion sublattice of oxide decomposes to form anion void at the site where the chemical potential of free electrons reaches the Fermi level of certain cations. These cations in anion void regroup to form a metallic phase. The high reducibility of solid carbon is explained by the exponential temperature dependence of the number of electrons emitted by it. This dependence takes place when the plasma flows around the surfaces of both reagents. The formation of carbide shells on the reagent surfaces is caused by the secondary interaction of carbon with a reduced metal on the oxide surface or of oxide lattice fragments with carbon on the corrosion resistance surface. The formation of carbide shells “poisons” the reagent surface and retards and stops reduction. This process renews after breaking the shells upon melting and flowing carbides. The detected laws manifest themselves during both direct and indirect reduction, make the concepts of both mechanisms closer, and eliminate the theoretical discrepancies observed between them in practice.

Prediction of Adsorption Isotherms of Multicomponent Gas Mixtures in Tight Porous Media by the Oil–Gas-Adsorption Three-Phase Vacancy Solution Model

For unconventional reservoirs, the effect of adsorption on phase equilibrium cannot be neglected because the process occurs in extremely tight porous media. This work focuses on the adsorption prediction of multicomponent mixture systems in tight porous media with the oil–gas-adsorption three-phase equilibrium model to a gas sample in the literature. The revisited vacancy solution model of adsorption by Bhatia and Ding is introduced to study the adsorption behaviors of the mixture. The gas and adsorbed phases are assumed to be the solutions of adsorbates with a hypothetical solvent called “vacancy”, and the vacancy is treated as an additional component engaged in the phase equilibrium in this theory. Instead of using parameters extracted from the multicomponent adsorption data, this method takes advantage because it accurately predicts the gas mixture adsorption equilibrium with consideration of non-ideal behavior in the adsorbed phase from pure gas adsorption isotherms over wide ranges of conditions, whi...

Analysis and study of CO2 adsorption on UiO-66/graphene oxide composite using equilibrium modeling and ideal adsorption solution theory (IAST)

In this paper, the equilibrium modeling of CO2 adsorption on the new adsorbent (composite of UiO-66 and graphene oxide) which has previously been reported in the experimental study has been investigated. For this purpose, in the first step, six adsorption isotherm models, including the Langmuir, Freundlich, BET, Toth, Dubinin–Astakhov and Maxwell–Stefan model coupled with vacancy solution theory (VST) have been used to fit the pressure dependent CO2 adsorption on the composite which has had the maximum CO2 uptake capacity (UiO-66/GO-5 composite) reported in the previous experimental study. Furthermore, Henry’s law constant for evaluating adsorption affinity of CO2 on this composite has been estimated by the Virial model. In the second step, the ideal adsorbed solution theory (IAST) solved with direct search minimisation has been used to predict the adsorption equilibrium of CO2/N2 binary gas mixture on UiO-66/GO-5 composite.

Adsorption equilibrium of methane and carbon dioxide on zeolite 13X: Experimental and thermodynamic modeling

A static, volumetric method has been used to determine the adsorption equilibrium of CH4 and CO2 and their binary mixtures on 13X molecular sieves at various temperatures between 273 and 343K. Pressures for the pure component data extend up to 10bar, while all binary data were obtained at 4bar and 6bar. The measured pure isotherms were regressed using different isotherm equations and the regressed parameters were applied to different thermodynamic models such as ideal adsorbed solution theory (IAST), vacancy solution theory (VST) and real adsorbed solution theory (RAST). CH4/CO2 system that deviate from ideality is not well represented by IAST and VST, whereas RAST which include activity coefficient in the adsorbed phase as characterizing parameter for non-ideality, show a much better representation of the binary equilibria. Experimental selectivities CO2/CH4 range from 26 to 2 at different pressure and temperatures. It is concluded that zeolite 13X suitable for natural gas industrial separation with yCO2<0.2 at 303K and 4bar. For landfill gas upgrading, where yCO2<0.45, zeolite 13X can be successfully applied at 303K, 4bar and 303K, 6bar and 323K, 4bar.

Modeling of single and competitive adsorption of cadmium and zinc onto activated carbon

This paper describes an experimental and modeling analysis of cadmium and zinc adsorption from aqueous solutions in single and binary systems on activated carbon. Batch tests were performed at constant pH (6.8 ± 0.3) and temperature (20 °C), in order to assess the adsorption capacity in experimental conditions simulating real wastewater. In particular, binary tests were carried out at same pH and temperature, with different initial concentration ratios of the two analytes (\(C_{Zn}^{0}\):\(C_{Cd}^{0}\)), in order to emphasize the competition phenomena while minimizing the effect of pH. Experimental results indicate that zinc is adsorbed to a greater extent than cadmium, both in single and binary systems. In binary systems, zinc adsorption capacity is not influenced by the presence of cadmium, regardless of its concentration. On the contrary, an increase in zinc concentration in solution brings about a decrease in cadmium adsorption capacity. The experiments were interpreted by using both the rigorous and the extended Langmuir multicomponent adsorption isotherms and the Vacancy Solution Theory. The latter provided a satisfactory and simultaneous description of the experimental data for both zinc and cadmium adsorption, also accounting for the possible interactions between the two analytes and between the solvent (water) and the single analyte.

Correlation of Adsorption Isotherms of Hydrogen Isotopes on Mordenite Adsorbents Using Reactive Vacancy Solution Theory

The authors applied the isotherm equations derived from the reactive vacancy solution theory to correlation of experimental and highly non-ideal adsorption isotherms of hydrogen and deuterium on a mordenite adsorbent, and examined the correlativity of the isotherm equations. The results reveal that the isotherm equations derived from the theory can better correlate the experimental isotherms.

CH4, C2H6, and C2H4 Phase Equilibria on SAPO-34 Using the Vacancy Solution Theory

Adsorption data of single, binary, and ternary mixtures of methane, ethane, and ethylene on Silicoalumina-Phosphate molecular Sieve (SAPO-34) were obtained experimentally in the pressure range of 0 to 600 kPa at 303, 313, and 323 K. The adsorbed equilibrium concentration was predicted based on the vacancy solution theory (VST) using excess Gibbs energy (EGE) models of activity coefficients. EGE models were studied comparatively, i.e., the Wilson, Flory Huggins, and NRTL equations. The VSM-model results were compared with the mixture adsorption data. The results revealed higher capability of EGE models against the extended Langmuir equation in predicting adsorption behavior of the so-called gas mixture.

Experimental Investigation and Thermodynamic Modeling of CH4/N2 Adsorption on Zeolite 13X

To implement an experimental study of CH4/N2 adsorption on Zeochem Co. zeolite 13X, a volumetric apparatus was utilized. In this regard, pure adsorption isotherms were measured at different temperatures [(273, 283, 303, 323, and 343) K] and pressures up to 10 bar, while binary data were collected at (303 and 323) K and different pressures and bulk gas phase molar fractions. Integral and differential thermodynamic consistency tests (TCT) were performed to validate the collected data and certify accuracy of the measurements. To have a thermodynamic view over the investigated system, thermodynamic functions such as enthalpy, entropy, surface potential, and Gibbs free energy were estimated numerically. Besides, the measured pure isotherms were regressed using different isotherm equations and the regressed parameters were applied to different models based on the thermodynamic theory of solutions, i.e., ideal adsorbed solution theory (IAST), vacancy solution models (VSM), and Peng–Robinson two-dimensional equat...

A modified multi-site occupancy model: evaluation of azeotropelike behavior in adsorption

Even though a large number of statistical-mechanics models can be found in the literature to describe adsorption, no one is good enough to reliably predict some highly non-ideal behavior, such as the inversion of selectivity presented in the adsorption of some mixtures. This is probably due to the natural complexity of adsorption phenomena, which can be attributed to several factors such as the non-uniformity of the solids and the intermolecular forces between adsorbent-adsorbate and adsorbate–adsorbate. In order to contribute to the improvement of the models, this paper presents a study of the impact of the relative molecule sizes and the lateral interactions for the azeotropelike behavior in adsorption. Therefore, we present here a modified model based on the Nitta et al. (1984) Multi-Site Occupancy Model (MSOM). The ability of the model proposed here to describe binary and ternary adsorption mixtures was compared to the one obtained from the original Nitta et al. (1984) model and by the Vacancy Solution Model (VSM, from Suwanayuen and Danner 1980a, b). The results showed that the relative size of the molecules and the lateral (adsorbate–adsorbate) interactions are very important variables in the description of the azeotropelike behavior. Even though the MSOM requires fewer parameters obtained from pure isotherm data, compared to VSM, it presented better performance for both binary and ternary mixtures. The proposed MSOM was able to predict the majority of the azeotropelike behavior studied here.

Gas adsorption separation of CO2/CH4 system using zeolite 5A

Pure gas adsorption isotherms of carbon dioxide at (273, 283, 303, 323, 343)K and binary adsorption isotherms of carbon dioxide and methane at (303, 323)K and pressures up to 10bar on Zeochem Co. Zeolite 5A were measured using a volumetric method. Equilibrium gas phase compositions have been determined using a gas chromatograph (GC). The experimental binary equilibrium data were compared with equilibrium data calculated by ideal adsorbed solution theory (IAST), and vacancy solution model (VSM). A model analysis of the experimental data has been performed with real adsorbed solution theory (RAST) owing to not satisfactory prediction of multi-component behavior with IAST and VSM. For this purpose, activity coefficients, accounting for the non-ideality of the adsorbed mixture, were calculated from the experimental data. The results of the pure experimental data showed that, the heat of adsorption for methane is approximately independent of loading (about 20kJ/mol), and for carbon dioxide decreases by increasing loading when q<0.5mol/kg. Subsequently, by increasing loading, the heat of adsorption increases up to q=2mol/kg. The selectivity of both simulated landfill and biogas mixtures have been also measured experimentally. These data indicated that zeolite 5A can be successfully applied in CO2/CH4 separation for landfill gas and biogas upgrading.

Pure and Binary Adsorption Equilibria of Methane and Nitrogen on Zeolite 5A

Adsorption isotherms of pure methane and nitrogen and their binary mixtures on Zeochem Co. zeolite 5A were measured using a static volumetric apparatus. Pure isotherms were measured at (273, 283, 303, 323, and 343) K and pressures up to 10 bar, while binary data were measured at (303 and 323) K and different pressures and bulk gas phase compositions. Experimentally measured data were validated using the integral thermodynamic consistency test. In contrast to the aforementioned binary measurements, predictions of different thermodynamic models utilizing pure adsorption isotherms were used to describe binary adsorption behavior of methane and nitrogen over zeolite 5A. Models based on the thermodynamic theory of solutions such as ideal adsorbed solution theory, vacancy solution models, and two-dimensional equations of state were used for this purpose. Experimental and predicted equilibrium data were compared through the appropriate phase diagrams. Predicted selectivity curves were compared against experiment...

The Generalized Maxwell-Stefan Model Coupled with Vacancy Solution Theory of Adsorption for Diffusion in Zeolites

It seems using the Maxwell-Stefan (M-S) diffusion model in combination with the vacancy solution theory (VST) and the single-component adsorption data provides a superior, qualitative, and quantitative prediction of diffusion in zeolites. In the M-S formulation, thermodynamic factor (Г) is an essential parameter which must be estimated by an adsorption isotherm. Researchers usually utilize the simplest form of adsorption isotherms such as Langmuir or improved dual-site Langmuir, which eventually cannot predict the real behavior of mixture diffusion particularly at high concentrations of adsorbates because of ignoring nonideality in the adsorbed phase. An isotherm model with regard to the real behavior of the adsorbed phase, which is based on the vacancy solution theory (VST) and considers adsorbate-adsorbent interactions, is employed. The objective of this study is applying vacancy solution theory to pure component data, calculating thermodynamic factor (Г), and finally evaluating the simulation results by comparison with literature. Vacancy solution theory obviously predicts thermodynamic factor better than simple models such as dual-site Langmuir.

Adsorption of lead (Pb2+) and uranium [formula omitted] cations by brown algae; experimental and thermodynamic modeling

Batch experiments were conducted to assess the effect of metal concentration and initial pH of solution on the biosorption of UO22+ and Pb2+ by chemical modified Cystoseira indica. The sorption capacity of Pb2+ was enhanced by increasing initial pH from 3.0 to 5.5 and maximum sorption of UO22+ biosorption was occurred around initial pH 4.0. The single metal isotherm data, at 25°C, were fitted on Langmuir equation and vacancy solution theory model using Flory–Huggins activity coefficients (VST-Flory–Huggins). The equilibrium adsorption experiments of the binary solution systems were carried out and the results were modeled by four types of extended Langmuir and multi-component VST-Flory–Huggins isotherm equations. Notwithstanding presence of any adjustable parameter, it was concluded that multi component VST-Flory–Huggins predicted the binary solution isotherms more accurate than extended Langmuir isotherms.

Reactive vacancy solution theory for correlation and prediction of adsorption equilibria for physical and chemical adsorptions

An isotherm equation was developed in the framework of the vacancy solution theory. In the model, vacancies in the adsorbed phase are dealt with as a kind of reactive entity, which leads to more flexible adsorption isotherm equations. The model can be called as reactive vacancy solution theory (RVST). Practical RVST equations for single-component and binary-component adsorption systems were derived by using Wilson, NRTL and UNIQUAC equations for activity coefficients. The RVST equations were found to coincide with the Langmuir–Freundlich equation when the effect of activity coefficients is assumed to be negligible. Furthermore, it was also found that the RVST model conforms to several simple-theoretical or empirical isotherm equations when the model is simplified. Therefore, it can be stated that the reactive vacancy solution theory can be regarded as more universal and general mathematical description of adsorption equilibria. Validity of the RVST equations for single-component adsorption was tested. The results reveal that the RVST-W and RVST-N equations can appropriately correlate non-ideal adsorption equilibrium data.

Development of Reactive Vacancy Solution Theory for Physical and Chemical Adsorptions

Development of Reactive Vacancy Solution Theory for Physical and Chemical Adsorptions

Pure and binary adsorption isotherms of ethylene and ethane on zeolite 5A

Pure and binary adsorption equilibrium data of ethylene and ethane on zeolite 5A were collected with a volumetric method for the temperature range 283 K to 323 K and pressure up to 950 kPa. The applicability of the binary adsorption prediction by the vacancy solution theory (VST) was investigated. Further individual adsorption and selectivity were obtained by VST prediction. According to the experimental results, zeolite 5A has a high adsorption capacity and selectivity for ethylene in the ethylene/ethane system. VST predicts that ethylene selectivity increases with pressure; it also shows that the amount of ethylene separated by zeolite 5A increases as the temperature decreases at a specified pressure.

Pure and mixed gas adsorption of CH4 and N2 on the metal–organic framework Basolite® A100 and a novel copper-based 1,2,4-triazolyl isophthalate MOF

Pure gas adsorption isotherms of CH4 and N2 and their binary mixtures were measured at 273 K, 298 K and 323 K and up to 2 MPa on two different microporous metal–organic frameworks (MOFs), i.e. the commercially available Basolite® A100 and the recently reported copper-based triazolyl benzoate MOF 3∞[Cu(Me-4py-trz-ia)] (1). The Toth isotherm model and the vacancy solution model were used to describe the experimentally determined isotherms and proved to be well suited for this purpose. While 1 shows a more homogeneous surface with a nearly constant isosteric heat of adsorption of 18–18.5 kJ mol−1 for CH4 and 12–15 kJ mol−1 for N2, the isosteric heat of adsorption at zero coverage for Basolite® A100 is 19 kJ mol−1 for CH4 and 16.2 kJ mol−1 for N2, decreasing significantly with increasing loading. Binary adsorption isotherms were measured gravimetrically to determine the total adsorbed mass of CH4 and N2. The van Ness method was successfully applied to calculate partial loadings from gravimetrically measured binary adsorption isotherms. Further studies by volumetric–chromatographic experiments support the good correlation between experimental data and predictions by the vacancy solution model (VSM-Wilson) and the ideal adsorbed solution theory (IAST) from pure gas isotherms. The experimental selectivities were determined to be αCH4/N2 = 4.0–5.0 for 1, slightly higher than for Basolite® A100 with αCH4/N2 = 3.4–4.5. These values are in good agreement with predictions for ideal selectivities based on Henry's law constants. From the experimental selectivities the potential of both MOFs in gas separation of CH4 from N2 can be derived.

Adsorption Thermodynamics in the Framework of the Modified Associate Formalism

A new thermodynamic model of adsorption of gas mixtures on microporous adsorbents is suggested. The model is based on Vacancy Solution Theory, while the recently proposed Modified Associate Formalism is used for adsorbed phase. The proposed model allows prediction of co-adsorption isotherms based on fitting those for pure gases.

Experimental and theoretical study of the adsorption of pure molecules and binary systems containing methane, carbon monoxide, carbon dioxide and nitrogen. Application to the syngas generation

This study takes place in the context of the use of a Synthesis Gas in Gas To Liquid process, liquid hydrocarbon production by conversion based on Fischer–Tropsch synthesis. Our aim is the process improvement by a selective recycling of the tail gas. So, we measure pure component isotherms for four gases (CO 2, CH 4, CO, N 2) of the tail gas until 2000 kPa and binary mixture (CO 2–CH 4; CO 2–N 2; CH 4–N 2) equilibria at 303.15 K and 400 and 950 kPa onto a ZSM-5 zeolite. We also predict the binary mixture equilibria by the Ideal Adsorbed Solution Theory (IAST) and the Vacancy Solution Model (VSM, Flory–Huggins and Wilson forms) and we obtain very good results. So not only binary mixture equilibria but also ternary and quaternary mixture adsorption can be predicted. With these data (experimental and simulated), we can conclude that the CO 2 is the most adsorbed component while N 2 is the least one. These two components can be separated from CH 4 and CO which are sent in the Synthesis Gas production step.