Extended Langmuir Equation Research Articles

Creep behavior of single coal particles based on uniaxial tests

The uniaxial creep test offers a robust approach for investigating the creep behavior of coal particles, while an empirical creep model based on the extended Langmuir equation accurately characterizes the creep curves. Prior to particle destruction, creep deformation progressively accumulates in three distinct stages with increasing load. Only when the diameter of particles exceeds a certain critical value, which is referred to as the matrix size, do both the crushing strength and effective elastic modulus exhibit size effects. The creep hardening effect results in a decrease in the matrix size of samples, leading to a significant increase in the effective elastic modulus of particles and an enhancement in the crushing strength of particles smaller than their original matrix size. The creep-induced damaging effect leads to creep failure in particles, resulting in a decrease in the crushing strength of particles with a diameter larger than the original matrix size.

Artificial neural network based optimization of a six-step two-bed pressure swing adsorption system for hydrogen purification

The pressure swing adsorption (PSA) system is widely applied to separate and purify hydrogen from gaseous mixtures. The extended Langmuir equation fitted from the extended Langmuir-Freundlich isotherm has been used to predict the adsorption isothermal of hydrogen and methane on the zeolite 5A adsorbent bed. A six-step two-bed PSA model for hydrogen purification is developed and validated by comparing its simulation results with other works. The effects of the adsorption pressure, the P/F ratio, the adsorption step time and the pressure equalization time on the performance of the hydrogen purification system are studied. A four-step two-bed PSA model is taken into consideration, and the six-step PSA system shows higher about 13% hydrogen recovery than the four-step PSA system. The performance of the vacuum pressure swing adsorption (VPSA) system is compared with that of the PSA system, the VPSA system shows higher hydrogen purity than the PSA system. Based on the validated PSA model, a dataset has been produced to train the artificial neural network (ANN) model. The effects of the number of neurons in the hidden layer and the number of samples used for training ANN model on the predicted performance of ANN model are investigated. Then, the well-trained ANN model with 6 neurons in the hidden layer is applied to predict the performance of the PSA system for hydrogen purification. Multi-objective optimization of hydrogen purification system is performed based on the trained ANN model. The artificial neural network can be considered as a very effective method for predicting and optimizing the performance of the PSA system for hydrogen purification.

Application of a dealginated seaweed derivative for the simultaneous metal ions removal from real and synthetic effluents

In this study, the alginate extraction residue (RES) from Sargassum filipendula was employed as biosorbent for the simultaneous removal of Cr3+, Ni2+ and Zn2+ from ternary synthetic solutions and for the decontamination of industrial (leather industry) and urban real effluents that were collected from different areas of Strasbourg (France). For this purpose, biosorption experiments in batch mode, multimetals equilibrium isotherms fitting and biosorbent characterization were carried out. In synthetic effluents, RES exhibited a greater affinity for Cr3+ ions, while a still unknown affinity for Al3+ and Pb2+ was verified for real conditions, reaching up to 80 % removal in some cases. At equilibrium, the higher sorption capacities were found at 50 °C as 0.864, 0.302 and 0.347 mmol/g for Cr3+, Zn2+ and Ni2+, respectively. Regarding the equilibrium models fitting, just the Extended Langmuir equation was able to describe the experimental data, showing an increase in qmax as the temperature rose, besides a decay in KL,1, KL,2 and KL,3 at the higher temperatures that indicates a weakening of adsorbent-adsorbate interactions. The characterization analyzes revealed a complex biosorption with a depth participation of carboxylic and hydroxyl groups was revealed by the characterization analyses, whereas the ion exchange mechanism played a really important role. The cation exchange capacity of RES was quantified as 34.12 mg/gRES with main exchangeable position of Ca2+ and Na+ ions. Based on these results, RES could be used as a novel and efficient biosorbent for toxic metals removal even from quite diluted real effluents, contributing to its valorization.

The binary gas sorption in the bituminous coal of the Huaibei Coalfield in China

Knowledge of the gas sorption characteristics of a coal not only helps to explain the mechanism of enhanced coalbed methane recovery but also provides an important basis for simultaneous coal and gas extraction. In consequence, the pure and binary gas excess sorption capacity of methane, carbon dioxide, and nitrogen of bituminous coal samples derived from the Xutuan Coal Mine in Huaibei coalfield, in Anhui Province in China, was measured using the volumetric method. The fitting analysis of the pure gas Langmuir adsorption model was carried out. The binary gas excess sorption measurement showed that the final sorption capacity of bituminous samples was the same no matter what the gas adsorption order of competitive adsorption and displacement adsorption. Hence, coal gas adsorption is physical adsorption, i.e. the different adsorption and desorption process of gas molecules does not affect the final adsorption amount of coal to each component of gas. Using the fitting parameters obtained by the Langmuir equation, the extended Langmuir equation was used to predict the adsorption capacity for each component of the binary gas. The comparison between predicted adsorption capacity and measured adsorption capacity showed that the extended Langmuir equation can better describe the trend of the adsorption isotherm curves of a binary gas under different pressures. The separation coefficient and displacement coefficient were defined from Langmuir adsorption theory. The separation coefficient involves the proportion of each component in the free phase and the proportion of each component in the adsorption phase. The displacement coefficient involves the displacement ability of gas molecules at adsorption sites by free gas molecules.

An explicit multicomponent adsorption isotherm model: accounting for the size-effect for components with Langmuir adsorption behavior

The extended Langmuir (EL) model is a popular multicomponent adsorption equilibria model, which can be based on single component Langmuir isotherms fitted on pure component data. Such explicit models are preferred over their implicit counterparts due to a lower computational requirement. An important shortcoming of the EL model is its inability to capture the adsorbate size effect occurring when the saturation capacities of pure component Langmuir isotherms are dissimilar. In contrast, this size effect is captured by the ideal adsorbed solution theory (IAST), which is centered on a set of implicit equations. In this work, we present an explicit multicomponent adsorption model for components with uneven saturation capacities obeying the Langmuir isotherm equation. This model predicts the expected change in selectivity with mixture composition, and even a selectivity reversal at high pressure when the adsorbates have significantly different molecular sizes. The model is extendable to any number of components, reduces to the Langmuir equation for pure components and to the EL equation when all saturation capacities are equal. The newly proposed model can be used to approximate the IAST and upgrade the EL model without introducing new parameters. Especially for binary mixtures, this model (Eqs. 12–14) offers a simple improvement of the EL model in predicting the experimental adsorption of light alkanes on 13X and 5A zeolites. The presented model is also applied to describe phase-changing adsorbents, in combination with the osmotic framework adsorbed solution theory (OFAST).

CO2-ECBM in coal nanostructure: Modelling and simulation

Coal is a porous media, and most pores in coal are nanopores (pores at the nanoscale). In order to investigate CO2-ECBM based on the nanostructure obtained by synchrotron radiation nano-CT at the Beijing Synchrotron Radiation Facility (BSRF), a nanopore structure-based CO2-ECBM model was developed, in which extended Langmuir Equation was applied to formulate the competitive adsorption mechanism of binary gas system of CO2-CH4 and gas ad/de-sorption and diffusion were coupled. CH4 and CO2 distribution in the coal nanostructure during the CO2-ECBM was visualized and the effect of CO2 injection pressure on methane recovery and CO2 sequestration was investigated. The increase of CO2 injection pressure enhances methane recovery and CO2 injection, but the contribution of CO2 injection pressure on methane recovery rate and CO2 injection rate becomes weaker with the increase of CO2 injection pressure. Because prior researches have shown that gas diffusivity varies with gas pressure, the impact of CO2 diffusion coefficient which varies with CO2 injection pressure on methane recovery and CO2 injection was investigated, and results show the variation of CO2 diffusion coefficient caused by the variation of CO2 injection pressure can explain why the increase of CO2 injection pressure can enhance CH4 recovery and CO2 injection. The difference in CO2 injection rate and CH4 recovery rate between different coal samples is related to the difference in gas diffusivity in different coal samples. CO2 injection rate and CH4 recovery rate is relatively higher in coal with higher gas diffusivity. The higher diffusion coefficient of CO2 caused by the lower kinetic diameter of CO2 can also help to explain why CO2 injection rate is larger than CH4 recovery rate. This study provides a new option to explore the CO2-ECBM at the nanopore scale.

Single and binary adsorption of reactive black 5 and Congo red on modified dolomite: Performance and mechanism

Adsorption of reactive black 5 (RB5) and Congo red (CR) by dolomite treated at 900°C (D900) was investigated in single and binary solutions. D900 was first characterized by laser granulometry, SEM, FTIR, and pore-size distribution analysis. Both adsorption, desorption, and regeneration of the adsorbent were examined. A particular interest has been focused on the spectroscopic study for elucidating the mechanism of the interaction of RB5/CR with D900. The latter favors the uptake of Congo red at the expense of reactive black 5 regardless of time. Extended Langmuir equation gives a good estimation of our binary data. Also, the experimental points agree with the plotted 3D-surfaces. A comparison between the single and binary modes highlights an antagonism between the RB5 and CR molecules, i.e., the components of the mixture are mutually hindered during adsorption. At equilibrium, CR is more strongly coadsorbed than RB5, viz. 229.18 against 72.37mgg−1 at 40°C, respectively. In this context, methanol desorbs 84% of RB5 and 76% of CR of their respective adsorbed capacity. Knowing that RB5 and CR contain one and two amine functions, respectively, the preferential adsorption of CR is explained via a mechanism of inner-sphere complexation, implying amine groups. Dolomite heated at 900°C could prove to be a valuable adsorbent when a discrimination in the adsorption of azo dyes is required.

Intermolecular interactions of 1,2-diethoxyethane with toluene: An insight from surface and volumetric properties at different temperatures

Densities and surface tensions of binary mixture of 1,2-diethoxyethane(DEE) and toluene have been measured over the entire composition at four temperatures of 293.15, 303.15, 313.15 and 323.15K and atmospheric pressure. The trends in measured densities and surface tensions with respect to composition and temperature are discussed in detail and provide complementary information to each other. Excess molar volumes VE and surface tension deviations Δσ of the mixtures are directly calculated from experimental results and well correlated using the Redlich–Kister polynomial equation, which provides a simple tool for interpolation of these properties with fairly high accuracy. Other thermodynamic properties of partial molar volumes, thermal expansion coefficients, surface entropy and enthalpy are also calculated. The sign and magnitude of these quantities are discussed in terms of the nature of intermolecular interactions present in binary mixtures. The negative excess volume properties suggest that the formation of hydrogen bonds between DEE and toluene molecules and the geometrical packing effect are most likely to give rise to the volume contraction during mixing. The surface tensions of the mixture at all temperatures exhibit negative aneotropies and negative Δσ, which is considered as the outcome of intermolecular interactions between DEE and toluene and the prevalent adsorption of toluene at surface, according to the molding results derived using the Extended Langmuir equation.

Investigation of heavy metal adsorption in binary system by nanocrystalline cellulose – Bentonite nanocomposite: Improvement on extended Langmuir isotherm model

The preparation of NCC – bentonite nanocomposite using waste paper as the source of NCC was conducted in this study. The adsorption performance of the composite was tested for the removal of Pb(II) and Hg(II) from aqueous solution in single and binary systems. Langmuir and Freundlich adsorption isotherms were employed to correlate pure component adsorption isotherm. Langmuir equation can represent the experimental data better than Freundlich, the qm for lead is higher than mercury in both systems (single system qm = 0.44 mmol/g (Pb) and 0.23 mmol/g (Hg) for composite). All systems exhibit endothermic process, except for bentonite which shows the exothermic process. The modification of extended Langmuir model for a binary system with the inclusion of fractional loading and heat of adsorption was proposed in this study. The modified extended Langmuir model could represent the experimental data better than original extended Langmuir equation.

Study of synthesis parameters of MIL-53(Al) using experimental design methodology for CO2/CH4 separation

In this study hydrothermal method was used to synthesize MIL-53(Al) (MIL stands for Materials Institute of Lavoisier). Plackett–Burman (P–B) as an experimental design method was applied to investigate the effect of synthesis and activation conditions on specific surface area, relative crystallinity, and production yield of MIL-53(Al) synthesis. Some parameters such as ligand-to-metal molar ratio, synthesis time, synthesis temperature, calcination temperature, and calcination time were selected as the variables. The Brunauer–Emmett–Teller (BET) technique was used in order to estimate the specific surface area of samples while the relative crystallinity of the samples was estimated by comparing their X-Ray Diffraction (XRD) pattern. The morphology of the samples was investigated by field emission scanning electron microscopy. The yield of final products was determined based on organic ligands. The results revealed the significant effect of synthesis temperature on BET surface area, particle size, yield, and crystallinity. The calcination temperature has significant positive effect on BET and crystallinity. Also, the negative significant effect of molar ratio on yield was concluded from the results. However, negligible effect of synthesis and calcination time on the properties of prepared materials were observed. Furthermore, separation capability of a selected sample for carbon dioxide (CO2) and methane (CH4) was measured. Pure gas adsorption data were successfully fitted to Langmuir, Sips, and Toth models. The selected sample provided high adsorption capacity for both gases. The binary adsorption of gases was also investigated based on extended Langmuir equations and the ideal adsorbed solution theory (IAST) models. Comparing the experimental and models data indicated good agreement between the IAST model and experiments. Finally, high CO2/CH4 selectivity of 7.6 was obtained experimentally for the CO2/CH4 molar ratio of 0.2/0.8.

Experimental study on history of methane adsorption capacity of Carboniferous-Permian coal in Ordos Basin, China

The knowledge of adsorption evolution in medium- to high-rank coal basins in China in the long history of tectonic subsidence and uplifting would be of great significance to the understanding of coalbed methane enrichment and accumulation. A model for calculating adsorption capacity history on major coal beds in Hancheng, the Ordos Basin, is established based on adsorption experiments in high-temperature high-pressure conditions with samples from medium- to high-rank coal reservoirs. Studies show that adsorption capacity on medium- to high-rank coal reservoirs is mainly dependent on several factors and is positively correlated with pressure and thermal evolution and negatively correlated with temperature, water content, ash content and volatile content. The model is an extended Langmuir equation mathematically built with temperature, pressure and thermal evolution and then used to reconstruct adsorption evolution on major coal reservoirs in Hancheng as per the burial history and thermal history. The results reveal three stages of adsorption in the geologic history, i.e. early steady stage with low adsorption, middle soaring stage, and late steady stage with high adsorption.

Fe(III) recovery from HCl solutions using amberlite XAD‐7 resin impregnated with a tetraalkyl phosphonium ionic liquid

AbstractFe(III) is efficiently extracted from concentrated HCl solutions using Amberlite XAD‐7 impregnated with tetraalkyl phosphonium chloride ionic liquid (IL) (synthesis of extractant‐impregnated resin, EIR). The sorption efficiency is controlled by metal speciation and IL loading in the EIR. Sorption isotherms in mono‐component solutions are described by the Langmuir equation, while the extended Langmuir equation perfectly fits sorption isotherms from binary Fe(III)/Zn(II) solutions. The thermodynamic study confirms the endothermic nature of the sorption. Uptake kinetics are fitted by the pseudo‐second order rate equation. While temperature and metal concentration have a relatively limited effect on kinetics, the IL content more significantly affects the mass transfer of Fe(III). Water, sodium sulphate, nitric acid, and sulphuric acid almost completely desorb Fe(III) from loaded EIRs. Resin recycling was tested for eight cycles without significant decrease of the sorption and desorption efficiencies.

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.

Kinetics and equilibrium adsorption of copper(II) and nickel(II) ions from aqueous solution using sawdust xanthate modified with ethanediamine

Sawdust xanthate modified with ethanediamine was used for the removal of Cu(II) and Ni(II) from aqueous solution. The influence of various operating parameters such temperature and adsorbent dosage on the adsorption isotherms of modified sawdust was investigated. Thermodynamic parameters, namely Gibbs free energy (ΔGΘ), enthalpy (ΔHΘ) and entropy (ΔSΘ) of Cu(II) and Ni(II) adsorption process were calculated, showing that the adsorption is a spontaneous and exothermic process. The modified extended Langmuir equation approaches provide excellent prediction of the binary adsorption. In single and binary systems, the overall adsorption data were best described by the pseudo-second order kinetic model, then the calculated values of activation energy of Cu(II) and Ni(II) adsorption process were 59.12 and 55.92 kJ/mol respectively. The results show that the affinity of each metal ion onto the modified sawdust surface is influenced by the presence of the other one.

Investigation on the montmorillonite adsorption of biocidal compounds incorporating thermodynamical-based multicomponent adsorption isotherm

Sublethal concentration of biocides, namely triclosan and benzalkonium chloride, have been known to raise severe environmental problems such as pathogens resistance and the existence of the toxic compounds in reclaimed water. Simple adsorption process of those biocides onto the bentonite modified by dodecyltricetyl ammonium bromide (DTAB) cation, show a remarkable increase on the removal efficiency of triclosan, regardless of the pH value. It was found that organophilic cation facilitates the anchoring of hydrophobic triclosan, but slightly limits the adsorption of benzalkonium chloride by occupying the active cation exchange site in the bentonite structure. Adsorption of a single system can be described properly by Langmuir isotherm equation. Incorporation of the Gibb’s free energy on the affinity constant of the extended Langmuir equation may attribute robust predictive ability on the binary adsorption model.

Adsorption of small organic solutes from beet distillery condensates on reverse-osmosis membranes: Consequences on the process performances

Reverse osmosis (RO) is an attractive process for the detoxification of distillery condensates before their recycling at the fermentation stage. However, transfer mechanisms through dense NF and RO membranes are still not well understood for the organic solutes to eliminate, and rejection results could be disappointing. This study aims at correlating the membrane and solute characteristics (polarity, surface charge, molecular weight, etc.) to the transfer results and further to the process performances. This was achieved through the study of the sorption isotherms of five target inhibitory compounds (acetic and butanoic acids, furfural, 2-phenethyl alcohol and 2,3-butanediol) on three commercial RO membranes (ESPA2, CPA2 and BW30), the compounds being alone as well as mixed in order to evaluate the competition effects. Results reveal that acetic acid and 2,3-butanediol develop few interactions with the membrane material while furfural and 2-phenethyl alcohol present strong sorption of Langmuir type. Extended Langmuir equation succeeded in accounting for the solutes’ sorption in mixtures insofar as acetic acid is not considered as competitor since it follows a different transfer mechanism. Coupled with their molecular weight (MW), low rejections obtained for acetic acid and furfural at pilot-scale as well as high rejection results for 2,3-butanediol and 2-phenylethanol could be explained.

Equilibrium isotherms studies for light hydrocarbons adsorption on 4A molecular sieve zeolite

Equilibrium adsorption isotherms were studied for pure methane, pure ethane, and methane, ethane, and propane mixture on 4A molecular sieve zeolite at 301 K. The constant-volume method was used for measuring the pure and the multi-component experimental equilibria data. Various isotherm models were utilized for correlation of pure and multi-component isotherm data. The pure component experimental data agreed well with the Langmuir and Freundlich equations. Both the extended Freundlich and modified extended Langmuir equations correlated the multi-component experimental data fairly well. The results of this study showed that ethane was more selectively adsorbed than methane on 4A molecular sieve zeolite, while propane was slowly adsorbed on this zeolite at the studied temperature. • Adsorption of pure and multi-component for methane, ethane and propane on 4A zeolite were studied. • Constant-volume method was adopted for measuring of data. • Langmuir and Freundlich equations correlate the pure component data fairly well. • Extended Freundlich and modified extended Langmuir provide good predictions for mixture data. • 4A zeolite had more affinity with ethane than methane, while it had low affinity with propane.

Multi-component adsorption in heterogeneous carbonaceous porous media through the integration of small-scale, homogenous models

In this work, a simplified multi-scale modeling approach to multi-component adsorption is developed. A number of binary gas systems involving CO2, CH4 and N2 adsorbed on carbon pores are analyzed in three scales. Comprehensive molecular simulations at the microscopic level using the GCMC method are the basis for the validation of the simplified (mesoscopic-level) models for isotherms of homogenous adsorbent. The macroscopic models are then formulated through the integration of the smaller scale models. Three contributions are made in this work. Firstly, it is demonstrated that the form of extended Langmuir equation can represent adsorption isotherms, developed by GCMC simulation in homogeneous micro-pores under mono-layer adsorption. Secondly, the methodology for the estimation of transferable pore-size distributions using optimization algorithms is successfully provided that more than one single component adsorption isotherm is used in computations. Finally, the extended dual-site Langmuir equation is justified as a suitable macroscopic model for multi-component adsorption on heterogeneous porous media with parameters estimated from small-scale models.

Prediction of multi component equilibrium isotherms for light hydrocarbons adsorption on 5A zeolite

Multi component equilibrium isotherms for the adsorption of propane, n-butane, and i-butane mixture on 5A zeolite at 303 K were obtained experimentally and theoretically. The constant-volume method was used for measuring the experimental equilibria data. Both the extended Freundlich and modified extended Langmuir equations correlated the multi component experimental data fairly well. The selectivity of 5A zeolite to adsorb gases was also studied. The results of this study showed that n-butane was more selectively adsorbed than propane on 5A zeolite, while i-butane was not adsorbed on this zeolite at the studied temperature. Also, it was found that an increase in partial pressure of n-butane decreases the adsorbed amount of propane, while the increase of partial pressure of propane has no effect on adsorbed amount of n-butane.

Evaluating Binary Sorption of Phenol/Aniline fromAqueous Solutions onto Granular Activated Carbon and Hypercrosslinked Polymeric Resin (MN200)

Sorption equilibrium of phenol and aniline onto the granular activated carbon and hyperreticulated un-functionalized polymeric resin (MN200) was investigated in single and binary component aqueous systems. Higher loading was obtained for aniline than phenol onto both sorbents, which is probably due to hydrophobic difference between both solutes and the greater electronic density of the aromatic ring of the aniline. Granular activated carbon reported larger uptake than resin MN200 for both solutes, which may be attributed to the better physical properties of the granular activated carbon, for instance, larger surface area. The experimental sorption could be properly described by the Langmuir and Freundlich isotherms. Five models for predicting the binary equilibrium sorption isotherm were compared in order to determine the best fit model to correlate binary experimental data: the extended Langmuir isotherm with and without a constant interaction factor, a simplified model based on the single equilibrium factors, the empirical extended Freundlich isotherm and the modified extended Langmuir equation, which considers the synergistic interactions between sorbate–sorbate and not only the competition between them defined by the extended Langmuir model. The modified extended Langmuir model provides the best agreement between predicted and experimental data indicating that the synergistic interactions between solutes play an important role in the binary phenol/aniline sorption system.