Ideal Adsorbed Solution Model Research Articles

Measurements and calculations of the equilibrium adsorption amounts of CO2\u2013N2, CO\u2013N2, and CO2\u2013CO mixed gases on 13X zeolite

Pressure swing adsorption (PSA) is one practical process for CO2 separation from the exhaust gases in various industries, such as blast furnace gas in steel works. For optimum design of the PSA process, precise estimation of the adsorption equilibrium of mixed gases is desired. The ideal adsorbed solution (IAS) model is a reliable model for this estimation. However, the IAS model requires convergent calculations, which significantly increase the calculation load, especially in dynamic PSA simulations. An analytical formula such as the extended Langmuir (EX-LM) equation is more useful for calculation of the equilibrium adsorption amounts of mixed gases. A drawback of this equation, however, is the uncertainty of the thermodynamic consistency and consequently the accuracy of the calculation results. In order to clarify the necessary conditions for application of the EX-LM equation as an approximation of the IAS model with Langmuir equation (IAS-LM model), both the analytical features and the estimation accuracy of these different methods were evaluated. To evaluate the accuracy of the equations, the equilibrium adsorption amount of mixed gases consisting of CO2, N2, and CO, which are the major gas components of blast furnace gas in steel works, on 13X zeolite were measured experimentally. The results confirmed that the accuracy of the EX-LM equation varies depending on the gas pressure and also the affinities of the adsorbates. Under higher gas pressure conditions, more reliable calculation results were obtained by the IAS-LM model.

Gas Sorption and the Consequent Volumetric and Permeability Change of Coal II: Numerical Modeling

The permeability of coalbed methane reservoirs may evolve during the recovery of methane and injection of gas, due to the change of effective stress and gas adsorption and desorption. Experimental and numerical studies were conducted to investigate the sorption-induced permeability change of coal. This paper presents the numerical modeling part of the work. It was found that adsorption of pure gases on coal was well represented by parametric adsorption isotherm models in the literature. Based on the experimental data of this study, adsorption of pure \(\hbox {N}_2\) was modeled using the Langmuir equation, and adsorption of pure \(\hbox {CO}_2\) was well represented by the N-Layer BET equation. For the modeling of CO\(_2\) & N\(_2\) binary mixture adsorption, the ideal adsorbed solution (IAS) model and the real adsorbed solution (RAS) model were used. The IAS model estimated the total amount of mixture adsorption and the composition of the adsorbed phase based on the pure adsorption isotherms. The estimated total adsorption and adsorbed-phase composition were very different from the experimental results, indicating nonideality of the CO\(_2\)–N\(_2\)–Coal-adsorption system. The measured sorption-induced strain was linearly proportional to the total amount of adsorption despite the species of the adsorbed gas. Permeability reduction followed a linear correlation with the volumetric strain with the adsorption of pure \(\hbox {N}_2\) and the tested CO\(_2\) & N\(_2\) binary mixtures, and an exponential correlation with the adsorption of pure \(\hbox {CO}_2\).

Molecular simulation and modelisation of methane/ethane mixtures adsorption onto a microporous molecular model of kerogen under typical reservoir conditions

The prediction of mixture adsorption is a challenging task in gas industry when dealing with shales for both resources prospect or production forecast. In this work, we used molecular simulation and models to study the adsorption of methane/ethane mixtures onto a mature kerogen model under typical reservoir conditions (338K, up to 20MPa). Using Molecular Dynamics, we first generated microporous structures of kerogen, representative of field samples. Monte Carlo simulations in the Grand Canonical ensemble were used to produce pure compound and mixture adsorption isotherms on these adsorbent structures. The ability to predict simulation results of the Ideal Adsorbed Solution model and a modified statistical mechanical derivation of the Extended Langmuir model have been studied at low pressures (up to 1MPa) where species are supposed ideal and at higher pressures (up to 20MPa) where species non-ideality is partially introduced in the models. At low pressures, the adsorption isotherms predicted by the two models are in good agreement with the results from molecular simulation, independently of the confinement. At higher pressures, this agreement is only valid for the less confined structures and worsened as the micropore size decreases.

Adsorption equilibria of bio-based butanol solutions using zeolite

1-Butanol can be produced by clostridial fermentations with acetone and ethanol as by-products. The butanol can be present up to ∼20 g L −1 depending on process conditions and microbial strain. The high-silica zeolite CBV28014 has been proven to adsorb butanol selective over water, while showing higher affinity for butanol than for acetone and ethanol. Multi-component acetone–butanol–ethanol (ABE) adsorption on CBV28014 has been modeled using a single site extended Langmuir adsorption model and the ideal adsorbed solution (IAS) theory model. The IAS model describes multi-component adsorption of ABE in synthetic mixtures and ABE in filtered fermentation broth by CBV28014 more accurately than the single site extended Langmuir model.

Single-component and competitive adsorption of levulinic/formic acids on basic polymeric adsorbents

The adsorption equilibria of single-component and binary mixtures of levulinic/formic acids in the aqueous solution on three different types of basic polymeric adsorbents were experimentally measured at 30 °C. Adsorption isotherms such as Langmuir, Freundlich and Sips were applied to correlate the single-solute adsorption data. Results demonstrated that the adsorption isotherms of both acids on all three adsorbents were best described by the Sips model, and that formic acid has higher adsorption capacity and stronger affinity on all three resins. The adsorption of binary mixtures of formic/levulinic acids reveals that formic acid is preferentially adsorbed and levulinic acid can be competitively displaced by formic acid. Binary Sips model and the ideal adsorbed solution (IAS) theory were employed to simulate the binary competitive adsorption data. The binary Sips model cannot predict the competitive adsorption behavior. The IAS model was successfully coupled with Sips isotherm parameters determined from single-component adsorption data to predict the binary competitive adsorption behavior of levulinic/formic acids on all three resins.

Comparison of adsorption models in reservoir simulation of enhanced coalbed methane recovery and CO 2 sequestration in coal

Coalbed methane is an important resource of energy. Meanwhile CO 2 sequestration in coal is a potential management option for greenhouse gas emissions. An attractive aspect to this process is that CO 2 is adsorbed to the coal, reducing the risk of CO 2 migration to the surface. Another aspect to this is that the injected CO 2 could displace adsorbed methane leading to enhanced coalbed methane recovery. Therefore, in order to understand gas migration within the reservoir, mixed-gas adsorption models are required. Moreover, coal reservoir permeability will be significantly affected by adsorption-induced coal swelling during CO 2 injection. Coal swelling is directly related to reservoir pressure and gas content which is calculated by adsorption models in reservoir simulation. Various models have been studied to describe the pure- and mixed-gas adsorption on coal. Nevertheless, only the Langmuir and Extended Langmuir models are usually applied in coal reservoir simulations. This paper presents simulation work using several approaches to representing gas adsorption, implemented into the coal seam gas reservoir simulator SIMED II. The adsorption models are the Extended Langmuir model (ELM), the Ideal Adsorbed Solution (IAS) model and the Two-Dimensional Equation of State (2D EOS). The simulations based on one Australian and one American coal sample demonstrated that (1) the Ideal Adsorbed Solution model, in conjunction with Langmuir model as single-component isotherm, shows similar simulation results as the ELM for both coals, with the IAS model representing the experimental adsorption data more accurately than the ELM for one coal and identically with the ELM for the other coal; (2) simulation results using the 2D EOS, however, are significantly different to the ELM or IAS model for both coal samples. The magnitude of the difference is also dependent on coal swelling and the well operating conditions, such as injection pressure.

Adsorption Equilibria of C8 Aromatic Liquid Mixtures on Y Zeolites Using Headspace Chromatography

Liquid phase adsorptive separations are found in several industrial applications such as the recovery of p‐xylene from its isomers. In this study, the headspace experimental technique was used to measure pure and multicomponent adsorption equilibria of liquid xylenes in Y zeolite. Data for pure‐component equilibrium were determined at temperatures between 80 and 120°C and correlated using the Extended Langmuir model. The parameters for pure components estimated from the correlated data showed good agreement with data reported in previous studies and relatively low deviations when compared to the experimental data dispersion. Using the pure‐component data, two models were tested for multicomponent (binary and quaternary) equilibrium correlation: Ideal Adsorbed Solution (IAS) model and Extended Langmuir Multicomponent model. The results from the IAS model did not conform well to the experimental results, indicating the existence of significant nonidealities in the system. The Extended Langmuir model predicted values generally in good agreement with the binary and quaternary experimental data measured using the Headspace technique.

Adsorption Equilibrium and Dynamics of C4 Olefin/Paraffin on π‐Complexing Adsorbent

Ag+ ion impregnated clay as a newly developed adsorbent was studied for 1‐butene separation from n‐butane. Equilibrium adsorption isotherms of pure components were measured at the temperature range from 25°C to 100°C and pressure up to 1200 mmHg. Experimental data of n‐butane and 1‐butene were correlated with various isotherm models. The best selectivity was shown at 80°C. Equilibrium capacities for 1‐butene and n‐butane at 80°C and 900 mmHg were 0.92 and 0.31 mmol/g, respectively. The average heats of adsorption for n‐butane and 1‐butene were found to be 6.6 and 13.3 kcal/mol, respectively. Diffusion of 1‐butene and n‐butane on this sorbent was fast, with 100% uptake reached within 15 min. The IAS model with Toth isotherm for pure component gave the best prediction results for both the n‐butane and 1‐butene compared to the other models used in the study. Binary adsorption equilibrium was well predicted by the Ideal Adsorbed Solution (IAS) model. The equilibrium adsorption ratio of 1‐butene/n‐butane in binary system was 14.87 and its selectivity was 6.71 at 80°C and 900 mmHg, when the mole fraction of 1‐butene in gas phase was 0.689. Experimental breakthrough curves were well predicted by a mathematical model, and the curves were steep enough to separate 1‐butene from n‐butane. Thus, it can be noted that Ag+ ion impregnated clay can be applied to the adsorptive separation of C4 olefin/paraffin.

Band splitting in overloaded isocratic elution chromatography: II. New competitive adsorption isotherms

The equations of two new binary competitive isotherms models are derived. The first of these models assumes that the isotherms of the two pure, single compounds have distinct monolayer capacities. Its derivation is based on kinetic arguments. The ideal adsorbed solution (IAS) framework was applied to derive the second model that is a thermodynamically consistent competitive isotherm. This second model predicts the competitive adsorption isotherm behavior of a mixture of two compounds that have single-component adsorption behavior following a BET and/or a Langmuir isotherms. Both models apply well to the binary adsorption of ethylbenzoate and 4- tert.-butylphenol on a Kromasil-C 18 column (with methanol–water, 62:38, v/v, as the mobile phase). The best single-solute adsorption isotherms of these two compounds are the liquid–solid extended multilayer BET and the Langmuir isotherms, respectively. The kinetic and thermodynamic new competitive models were compared, regarding the accuracy of their prediction of the elution band profiles of mixtures of these two compounds. A better agreement between experimental and calculated profiles was observed with the kinetic model. The IAS model failed because the behavior of the ethylbenzoate/4- tert.-butylphenol adsorbed phase mixture is probably non-ideal. The most striking result is the qualitative prediction by these models of the peak splitting of 4- tert.-butylphenol during its elution in presence of ethylbenzoate.

New thermodynamically consistent competitive adsorption isotherm in RPLC

A new equation of competitive isotherms was derived in the framework of the ideal adsorbed solution (IAS) that predicts multisolute adsorption isotherms from single-solute isotherms. The IAS theory makes this new isotherm thermodynamically consistent, whatever the saturation capacities of these single-component isotherms. On a Kromasil-C 18 column, with methanol–water (80/20 v/v) as the mobile phase, the best single-solute adsorption isotherm of both toluene and ethylbenzene is the liquid–solid extended multilayer BET isotherm. Despite a significant difference between the monolayer capacities of toluene (370 g/l) and ethylbenzene (170 g/l), the experimental adsorption data fit very well to single-component isotherms exhibiting the same capacities (200 g/l). The new competitive model was used for the modeling of the elution band profiles of mixtures of the two compounds. Excellent agreement between experimental and calculated profiles was observed, suggesting that the behavior of the toluene–ethylbenzene adsorbed phase on the stationary phase is close to ideal. For example, the concentrations measured for the intermediate plateau obtained in frontal analysis differ by less than 2% from those predicted by the IAS model.

Robust design of countercurrent adsorption separation processes: 5. Nonconstant selectivity

AbstractOperating conditions for the separation of a binary mixture using a nonadsorbable eluent through simulated moving‐bed technology were designed. The results obtained using equilibrium theory for adsorption described by Langmuir models lead to the definition of explicit constraints on the operating parameters to operate the unit in the desired regime of separation. A more general approach was able to produce the same result for a larger class of isotherms. The physical and mathematical conditions defining this larger class of isotherms are discussed, as well as the algorithms necessary to calculate the region of complete separation. Applications to the bi‐Langmuir isotherm and the ideal adsorbed solution model, which are more flexible than the Langmuir model and can describe systems where selectivity changes with composition, are discussed. A shortcut method to get an explicit, though approximate, solution is proposed and its accuracy is discussed.

Performance analysis of four‐bed H2 PSA process using layered beds

AbstractHydrogen purification from a typical cracked gas mixture (H2/CO2/CH4/CO) by the four‐bed PSA process was studied experimentally and theoretically using layered bed of activated carbon and zeolite 5A. The mathematical model accounts for the mass and heat transfer resistance using the linear driving force approximation for the particle uptake, and the ideal adsorbed solution model represents the multicomponent adsorption equilibrium. Effects of the superficial velocity, heat transfer resistance and the bed layering on the process performance were investigated. Since the recovery sharply decreases above a certain productivity at the given purity, the relation between the productivity and recovery was studied before the process design. Its performance decreased with the increase in heat transfer resistance, but increased with heat transfer resistance in some range. Both the experiment and theory showed optimum carbon‐to‐zeolite ratios. Those optimum ratios depend on such operating variables as the superficial velocity, heat transfer resistance and product purity. For higher product purity more zeolite was used. As the superficial velocity increased, the process performance has its maximum at higher carbon‐to‐zeolite ratio. Except for the adiabatic conditions, the optimum carbon‐to‐zeolite ratio increased with the increase in the heat transfer resistance. At the adiabatic conditions, however, the optimum carbon‐to‐zeolite ratio was lower than that at the nonisothermal conditions.

Adsorption Equilibria of Krypton, Xenon, Nitrogen and Their Mixtures on Molecular Sieve 5A and Activated Charcoal

The adsorption equilibria of Kr, Xe and N2, which are constituents of the off-gas from nuclear reprocessing processes, on representative adsorbents (Molecular Sieve 5A (MS5A) and activated charcoal) were studied. Adsorption experiments were conducted in the temperature range of 77 to 323 K using a packed bed column. The adsorption isotherms for the activated charcoal adsorbent were successfully correlated by the vacancy-solution model. The adsorption isotherms for the MS5A adsorbent were properly correlated by the Langmuir model and the vacancy solution model. The adsorption experiments for the binary component systems (Kr—Xe, Kr—N2 systems) were also performed, and the results suggest that the coexistence of Xe greatly inhibits the adsorption of Kr. The coexistence of large amounts of N2 was also found to inhibit the adsorption of Kr. The experimental results for the adsorption equilibrium of binary component systems on the activated charcoal adsorbent were well reproduced by the vacancy solution model without parameter fitting. The binary adsorption equilibrium on the MS5A adsorbent is rather well predicted by the ideal adsorbed solution model without parameter fitting. The use of the vacancy solution model for this adsorption system requires the optimization of parameters, but the binary adsorption equilibrium is well reproduced with the optimized parameters.

99/00372 Study of coal gasification via neural networks

Coalbed methane is an important resource of energy. Meanwhile CO2 sequestration in coal is a potential management option for greenhouse gas emissions. An attractive aspect to this process is that CO2 is adsorbed to the coal, reducing the risk of CO2 migration to the surface. Another aspect to this is that the injected CO2 could displace adsorbed methane leading to enhanced coalbed methane recovery. Therefore, in order to understand gas migration within the reservoir, mixed-gas adsorption models are required. Moreover, coal reservoir permeability will be significantly affected by adsorption-induced coal swelling during CO2 injection. Coal swelling is directly related to reservoir pressure and gas content which is calculated by adsorption models in reservoir simulation. Various models have been studied to describe the pure- and mixed-gas adsorption on coal. Nevertheless, only the Langmuir and Extended Langmuir models are usually applied in coal reservoir simulations. This paper presents simulation work using several approaches to representing gas adsorption, implemented into the coal seam gas reservoir simulator SIMED II. The adsorption models are the Extended Langmuir model (ELM), the Ideal Adsorbed Solution (IAS) model and the Two-Dimensional Equation of State (2D EOS). The simulations based on one Australian and one American coal sample demonstrated that (1) the Ideal Adsorbed Solution model, in conjunction with Langmuir model as single-component isotherm, shows similar simulation results as the ELM for both coals, with the IAS model representing the experimental adsorption data more accurately than the ELM for one coal and identically with the ELM for the other coal; (2) simulation results using the 2D EOS, however, are significantly different to the ELM or IAS model for both coal samples. The magnitude of the difference is also dependent on coal swelling and the well operating conditions, such as injection pressure.

Modified van der Waals Equation for the Prediction of Multicomponent Isotherms

A modified two-dimensional van der Waals equation model was proposed for the prediction of multicomponent gas–solid adsorption isotherms from corresponding single-component adsorption equilibrium data. The model was used to predict adsorption isotherms of CO–CO2mixtures and CO2–N2mixtures on Cu(I)–NaY zeolite. Experimental adsorption equilibrium data of the two systems were compared with results calculated from the model and three other models in the literature: the ideal adsorbed solution model, the vacancy solution theory of adsorption using the Flory–Huggins activity coefficient equation, and the two-dimensional van der Waals equation. The results indicated that the modified van der Waals equation predicted the experimental results better than the three other models for the two systems studied, especially for the CO–CO2system, which involved chemical reaction during adsorption and exhibited azeotropic behavior.

Competitive adsorption of xenon and krypton in zeolite NaA: 129Xe nuclear magnetic resonance studies and grand canonical Monte Carlo simulations

Investigation of competitive adsorption is carried out using the Xe–Kr mixture in zeolite NaA as a model system. The XenKrm clusters are trapped in the alpha cages of this zeolite for times sufficiently long that it is possible to observe individual peaks in the nuclear magnetic resonance (NMR) spectrum for the clusters. The 129Xe nuclear magnetic resonance spectra of several samples of varying Xe and Kr loadings have been observed and analyzed to obtain the 129Xe chemical shifts and the intensities of the peaks which are dependent on the average krypton and xenon occupancies. The detailed distributions, f(XenKrm), the fractions of cages containing n Xe atoms and m Kr atoms can be observed directly in this system from the relative intensities since individual peaks for XenKrm mixed clusters are observed in the NMR spectrum. Grand canonical Monte Carlo (GCMC) simulations of mixtures of Xe and Kr in a rigid zeolite NaA lattice provide the detailed distributions and the average cluster shifts. The agreement with experiment is excellent. The calculated absolute chemical shifts for the Xen peaks and XenKr peaks at 300 K are in good agreement with experiment. A strictly statistical model of a binary mixture, derived from the hypergeometric distribution, in which the component atoms are distinguishable but equivalent in competition for eight lattice sites per cage under mutual exclusion provides a limiting case for the distributions, with which the GCMC simulations and the properties of the actual Xe–Kr system may be compared. The selectivity coefficients of the Xe–Kr mixture in zeolite NaA is well described by the ideal adsorbed solution model.

Analysis of isotachic patterns in displacement chromatography

Most previous theoretical treatments of displacement chromatography have been confined to systems that follow the competitive Langmuir isotherm. With the assumption of such idealized multi-component adsorption behavior, in a sufficiently long column the final outcome of the process is always expected to be an isotachic displacement train having a series of adjacent separated bands of increasing concentration. Several recent reports, however, suggest that no such train forms when the single-component isotherms of the separands cross. In order to examine the possibility of separation under such conditions, the stability of the isotachic pattern is analyzed and criteria for displacement and for stability of the resulting boundaries are established. The approach requires the knowledge of the multi-component isotherm that governs the adsorption of the separands. As the competitive Langmuir isotherm completely fails to represent such behavior, the pertinent multi-component isotherms are generated from Langmuir single-component isotherms within the framework of the ideal adsorbed solution model. The results obtained with such a multi-component isotherm in binary separations show that three operating regions in displacement chromatography can be identified when the single-component isotherms of the separands cross. In one region at sufficiently low concentrations, the two components separate and appear in the same order as in linear chromatography. In a second region at sufficiently high concentrations, the bands are predicted to separate but appear in the reverse order. In the third region at intermediate concentrations, complete separation is not possible, and the resulting isotachic pattern contains a mixed zone. The stability analysis presented here facilitates the prediction of the outcome of displacement without the need for arduous computation; it is fairly general and may be applied to systems that follow other multi-component isotherms.

Use of the LeVan—Vermeulen isotherm model for the calculation of elution band profiles in non-linear chromatography

The two-term LeVan—Vermeulen isotherm is the simplest competitive isotherm based on the ideal adsorbed solution model. It applies when both components follow individually the single-component Langmuir isotherm model. It takes into account the influence of the difference in the column saturation capacity for these two components. Individual band profiles calculated with this isotherm are in qualitative agreement with experimental results. They exhibit a stronger displacement effect, a weaker tag-along effect and a higher degree of band separation than predicted by the Langmuir competitive isotherm when the column saturation capacity is larger for the second component than for the first. Conversely, when the column saturation capacity is larger for the first component than for the second, the displacement effect is less intense and the tag-along effect is stronger than with the competitive Langmuir isotherm and the separation deteriorates. When the sample size is increased, a reversal of the elution order is observed.

Nonideal adsorption from multicomponent gas mixtures at elevated pressures on a 5A molecular sieve

Single component adsorption isotherms for H 2, CH 4, CO and CO 2 at pressures upto 800 psia, and multicomponent adsorption equilibria for various mixtures of these gases at 214 and 314 psia were measured on a 5A molecular sieve at 298 and 373 K. The extended Langmuir (EL) and ideal adsorbed solution (IAS) models were tested against the data. The predictions from these models were very similar. The IAS model also showed that the binary data exhibited considerable nonideal adsorbed solution (NAS) behavior which was further demonstrated from the experimental adsorbed phase activity coefficients and from the correlation with the spreading pressure-dependent (SPD) NAS model. Strong negative deviations from Raoult's law were generally exhibited; however, moderate positive deviations from Raoult's law also occurred from one of the components in some systems. In addition, the effects of gas phase nonidealities on the experimental adsorbed phase activity coefficients, and on the component loadings and adsorbed phase activity coefficients obtained from the SPD-NAS models, were studied. In both cases, the effects were significant only for the activity coefficients of systems which exhibited markedly different single component isotherms.

Activated carbon adsorption of diethanolamine, methyl diethanolamine and their degradation products

Batch experiments were conducted to determine the adsorption of diethanolamine, methyl diethanolamine and their major degradation products from aqueous solutions by a lignite based (DARCO) and a bituminous coal based (SGL) carbon. The former was virtually ineffective whereas the latter adsorbed all organic compounds well, but its adsorptive capacity was extremely low (typically less than 3 m mol/g carbon). Adsorption isotherms were established for SGL carbon and used to predict, by means of Wang and Tien's Ideal Adsorbed Solution model, breakthrough curves for column adsorbers. The predictions agreed well with experimental measurements. It was found that saturated SGL carbon could not be regenerated by heating to 300°C, but HCl or HNO 3 treatment restored its adsorptive capacity to about 50% or 70%, respectively, of the original value.