On the use of the dual process Langmuir model for predicting unary and binary isosteric heats of adsorption

Analytic expressions for unary and binary isosteric heats of adsorption as a function of the adsorbed phase loading were derived from the dual process Langmuir (DPL) model using the Clausius-Clapeyron equation. Unary isosteric heats of adsorption predicted from these expressions for several adsorbate-adsorbent systems were compared to values in the literature predicted from the well-accepted graphical approach using Toth and unilan models (Adsorption Equilibrium Data Handbook; Prentice Hall: NJ, 1989). Predictions from the DPL model were also compared to rare experimental unary and binary isosteric heats of adsorption in the literature for another adsorbate-adsorbent system. In all cases, very good agreement was obtained, showing that the DPL model can be used in adsorption process modeling for accurately predicting not only ideal and nonideal mixed-gas adsorption equilibria (Langmuir 2011, 27, 4700), but also unary and even binary isosteric heats of adsorption.     

Prediction of ternary phase equilibria from binary data

The two-parameter UNIQUAC equation is modified to give better results of vapor—liquid and liquid—liquid equilibria for a variety of binary systems. The proposed equation is easily extended to a multicomponent system without including any ternary (or multicomponent) parameters. The good capability of the equation in data reduction is shown by many illustrative examples for various kinds of strongly nonideal binary and ternary mixtures.     

Heterogeneous extended langmuir model with multiregion surfaces for adsorption of mixtures

The multiregion or multisite adsorption theory is applied to the heterogeneous extended Langmuir (HEL) model for predicting adsorption from mixtures. A new model, multiregion HEL (MR-HEL), is derived. MR-HEL is thermodynamically consistent. It uses the same three parameters for each component of the mixture as in the HEL model. Examples, including eight binary and one ternary systems, show that both MR-HEL and HEL yield satisfactory results for relatively ideal systems with like components. For nonideal and highly nonideal mixtures, however, MR-HEL reduces the total average deviation for the predicted amount adsorbed for each component by more than 50% in comparison with the original HEL model. The improvement by MR-HEL is significant. Moreover, the new model predicts not only an azeotrope for binary system CO(2)+C(3)H(8) that shows strong nonideal behavior but also the correct azeotropic composition.     

Adsorption equilibria of binary gas mixtures on graphitized carbon black

Adsorption equilibria for binary gas mixtures (methane-carbon dioxide, methane-ethane, and carbon dioxide-ethane) on the graphitized carbon black STH-2 were measured by the open flow method at 293.2 K. The experimental pressure range was (0 to 1.6) MPa. The extended Langmuir (EL) model and the ideal adsorption solution theory (IAST) have been adopted to predict the equilibria of binary gas mixtures. The results indicate that gas mixtures adsorbed on the homogeneous surface of STH-2 exhibit the nonideal behavior, which is mainly induced by adsorbate-adsorbate interactions. The real adsorption solution theory (RAST) has been used to analyze the property of the adsorbed mixtures. The activity coefficients have been correlated with the Wilson equation. The investigation demonstrates that the nonideality of adsorbed phase is completely dissimilar with the bulk liquid phase. The adsorption of the heavier component would benefit the adsorption of the lighter component.     

The prediction of isothermal phase equilibria for non-ideal multicomponent mixtures from heats of mixing

A method is presented for predicting both vapor—liquid and liquid—liquid equilibria for multicomponent mixtures using heat of mixing data for the constituent binary pairs together with pure component vapor pressures. Its application to two highly non-ideal hydrocarbon ternary systems is discussed. The parameters of the hybrid local composition model of Renon and Prausnitz, known as the NRTL equation, were evaluated from heat of mixing data for the three binary pairs in each of the two ternary systems. The parameters thus obtained were used in the multicomponent form of the NRTL equation to predict the ternary vapor—liquid equilibrium data for the completely miscible system cyclohexane(1)—n-heptane(2)—touluene(3) and for the partially miscible system acetonitrile(1)—benzene(2)—n-heptane(3) without the need for any ternary or higher order parameters.This method predicted compositions of the single phase region of the partially miscible ternary system with a standard deviation of 10%. It also predicted compositions for the fully miscible system with a standard deviation of 4.6%. Total pressure curves for the partially miscible and miscible ternaries were predicted with standard deviations of 6.6% and 4.5% respectively. Poor predictions of the binodal curve for the partially miscible region were obtained. The method offers a means of predicting the whole range of ternary phase equilibria for miscible systems.     

Correlation and Calculation of Multicomponent Adsorption Equilibria Data Using a Generalized Adsorption Isotherm

Enhanced by the need for reliable and accurate data of multicomponent gas adsorption equilibria on porous solids like activated carbons or zeolites, a new method to measure and correlate coadsorption equilibria has been developed. This method is a combination of gravimetric or volumetric measurements of the total load of pure or multicomponent adsorbates (Staudt, 1994; Gregg and Sing, 1982) and a correlation and calculation procedure using a new adsorption isotherm (AI) (Keller, 1990). This AI is thermodynamically consistent and describes adsorbates with fractal dimension for single- or multicomponent systems and load dependent adsorption energies. This method allows calculation of partial loads of multicomponent coadsorption equilibria from pure component data and the total loads of the mixture adsorption equilibria. This will be demonstrated for binary and ternary adsorption equilibria of CH₄, C₂H₄ and C₂H₆ on activated carbon (Reich et al., 1980).     

Effects of molecular siting and adsorbent heterogeneity on the ideality of adsorption equilibria

The ideal adsorbed solution (IAS) theory is the benchmark for the prediction of mixed-gas adsorption equilibria from pure-component isotherms. In this work, we use atomistic grand canonical Monte Carlo simulations to test the effects of molecular siting and adsorbent energetic heterogeneity on the applicability of the IAS theory. Pure-component isotherms generated by atomistic simulation are used to predict binary isobaric isotherms using the IAS theory. These predicted isotherms are compared with those obtained by a full atomistic simulation of the binary mixture. Binary mixtures of argon, methane, and CF4 in silicalite are found to obey IAS theory, while benzene/methane and cyclohexane/methane in silicalite are nonideal. The mixture of argon and CF4 is ideal despite the large difference in the sizes of the two species. This contradicts previous hypotheses in the literature, which state that mixtures of species of unequal size do not adsorb ideally. The nonideal behavior of the benzene/methane and cyclohexane/methane systems occurs because of adsorbent heterogeneity in these systems, which depends on both sorbent and sorbate. In addition, we use a lattice gas model with parameters derived from atomistic simulation to demonstrate analytically that a sufficiently energetically heterogeneous adsorbent will result in the breakdown of IAS theory even in the absence of interactions between sorbates.     

Liquid-liquid equilibria for the acetonitrile + methanol + saturated hydrocarbon and acetonitrile + 1-butanol + saturated hydrocarbon systems

Tie-line results at 25°C and atmospheric pressure are presented for {(acetonitrile + methanol) + cyclohexane, or + n-hexane, or + n-heptane or + n-octane} and for {(acetonitrile + 1-butanol) + cyclohexane, or + n-hexane or + n-heptane}. Vapor-liquid equilibria for acetonitrile + methanol at 25° C are reported. The UNIQUAC associated-solution model is used to correlate binary vapor-liquid equilibria and mutual solubilities for the 13 systems constituting the ternary systems and to predict the ternary liquid-liquid equilibria by using binary parameters alone.     

Correlation of liquid-liquid equilibria in aqueous and organic systems using a modified Wilson model

A modified Wilson model is extended to involve three ternary parameters per ternary to allow the model to represent ternary liquid-liquid equilibria accurately. The calculated results for 19 ternary systems obtained from the present modification are compared with the previous results obtained from other modified Wilson models. The model is further extended to treat quaternary liquid-liquid equilibria for six aqueous systems and one nonaqueous system using binary, ternary, and quaternary parameters. Mutual solubilities for 19 systems over a wide temperature range are represented with the model having temperature-dependent energy parameters.     

Ternary liquid—liquid equilibria and their representation by modified NRTL equations

Experimental liquid—liquid equilibrium data are reported for the systems acetonitrile—acetone—cyclohexane at 318.15 K and acetonitrile—methyl acetate—cyclohexane at 313.15 K. Two modified forms of the NRTL equation proposed by Renon are presented by substituting local surface fractions for local mole fractions and further by including Guggenheim's combinatorial entropy for athermal mixtures whose molecules differ in size and shape. The resultant equations involve three adjustable parameters and are extended to multicomponent systems without adding ternary (or higher) parameters. Calculated results of vapor—liquid and liquid—liquid equilibria for typical binary and ternary mixtures are presented.     

Empirical Multicomponent Equilibrium and Film-Pore Model for the Sorption of Copper,Cadmium and Zinc onto Bone Char

The adsorption of three metal ions onto bone char has been studied in both equilibrium and kinetic systems. An empirical Langmuir-type equation has been proposed to correlate the experimental equilibrium data for multicomponent systems. The sorption equilibrium of three metal ions, namely, cadmium (II) ion, zinc (II) ion and copper (II) ion in the three binary and one ternary systems is well correlated by the Langmuir-type equation. For the batch kinetic studies, a multicomponent film-pore diffusion model was developed by incorporating this empirical Langmuir-type equation into a single component film-pore diffusion model and was used to correlate the multicomponent batch kinetic data. The multicomponent film-pore diffusion model shows some deviation from the experimental data for the sorption of cadmium ions in Cd-Cu, Cd-Zn and Cd-Cu-Zn systems. However, overall this model gives a good correlation of the experimental data for three binary and one ternary systems.     

The prediction of isobaric phase equilibria for non-ideal multicomponent mixtures from heat of mixing data

A method for predicting isobaric binary and ternary vapor—liquid equilibrium data using only isothermal binary heat of mixing data and pure component vapor pressure data is presented. Three binary and two ternary hydrocarbon liquid mixtures were studied. The method consists of evaluating the parameters of the NRTL equation from isothermal heat of mixing data for the constituent binary pairs. These parameters are then used in the multicomponent NRTL equation to compute isobaric vapor—liquid equilibrium data for the ternary mixture. No ternary or higher order interaction terms are needed in the ternary calculations because of the nature of the NRTL equation. NRTL parameters derived from heat of mixing data at one temperature can be used to predict vapor—liquid equilibrium data at other temperatures up to the boiling temperature of the liquid mixture.For the systems studied this method predicted the composition of the vapor phase with a standard deviation ranging from 1–8% for the binary systems and from 4–12% for the ternary systems.     

Measurement of thermodynamic equilibria by chromatography

Summary After a brief recall of the chromatographic principles, the different applications of gas chromatographic measurements of thermodynamic equilibria were reviewed. Gas and liquid chromatographies are now well known and elegant methods for measuring the physicochemical properties and phase equilibrium thermodynamic constants. Although fundamentally a dynamical method and mostly known as a powerful separation technique, chromatography can be schematized by a sucession of equilbria of a chemical species partitioning between a mobile phase and a fixed liquid or solid stationary phase. It can be operated in either infinite dilution or finite concentration conditions and permits to collect a large number of data for calculating molecular interactions for solutes which are either rare or available at the trace level. Gas chromatography permits the measurement of gas adsorption isotherm, gas-liquid equilibria, molecular diffusion and interaction virials. The modelization of successive partition equuilibria occuring in the chromatographic column leads to rather simple expression of differential enthalpy, entropy, free energy of adsorption or solution, variation of heat capacity, complexation constant, second virial coefficients, gas-solid and gasliquid isotherm and also binary or ternary equilibria. The possibilities of High Performance-Liquid Chromatography to investigate adsorption from solutions and chemical equilibria are also discussed.     

Vapor-liquid and liquid-liquid equilibria of water, 2-methoxyethanol and cyclohexanone: Experiment and correlation

Vapor-liquid equilibria and liquid-liquid equilibria of a ternary mixture consisting of water, 2-methoxyethanol and cyclohexanone and in addition of all binary subsystems were studied experimentally at several temperatures. A ternary corrective term in the expression for the Gibbs free energy based on the NRTL model improves simultaneous representation of binary and ternary phase equilibria.     

Synergistic effects in competitive adsorption of carbohydrates on an ion-exchange resin

Adsorption of the three carbohydrates sucrose, glucose and fructose from aqueous solutions was investigated on an ion-exchange resin. The adsorption equilibrium of single components, binary and ternary mixtures was quantified by frontal analysis and the adsorption-desorption method. The experiments covered a concentration range up to 600 g/L at 60 degrees C and 80 degrees C. Within this range the adsorption isotherms of carbohydrates exhibited anti-Langmuirian behavior. Data of mixture adsorption revealed reversed competitive (synergistic or cooperative) effects, i.e., an increase of the concentration of one component of the mixture enhanced the adsorption of others. To model such an adsorption behavior the anti-Langmuir model has been used. The isotherm parameters determined for single components were used to simulate the competitive adsorption equilibria through the IAS (ideal adsorbed solution) theory. Finally, dynamic concentration profiles of multicomponent mixtures have been recorded. The shapes of adsorption and desorption curves confirmed the observed competitive effects found in the equilibrium studies. The breakthrough curves measured were simulated using the equilibrium theory as well as a numerical solution of the equilibrium dispersive model.     

Prediction of multicomponent liquid adsorption using excess quantities. II. Calculations for the liquid/solid interface

The utilization of excess quantities as the basis for a thermodynamic approach can simplify the prediction of multicomponent liquid adsorption from binary data. A new method for predicting liquid adsorption on solids is suggested, which is different from the existing equations with respect to the theoretical background and formulation. The applicability of the new model is tested with three ternary adsorption systems. The predicted surface excesses are discussed and compared with experimental ones and with those of other prediction models in the literature. The accordance between measured and predicted ternary data is convincing.     

A semi-empirical equation of state applied to vapor-liquid equilibria calculations

A five-parameter equation of state is proposed to calculate the vapor-liquid equilibria of compounds in binary and multicomponent mixtures. This equation is closely related to a previous equation of state proposed by the author, the main modification being in the entropic term where the parameter m assumes a constant value for all compounds. It is shown that the van der Waals conditions at the critical point and the Morbidelli-Carra' algorithm enable the calculation of three other constants. Rules are given to calculate the remaining constant K which pertains to the enthalpic term. The proposed method only requires knowledge of the critical constants and of the normal boiling temperature as input parameters. A wide application of the new equation to both polar and non-polar binary systems indicates the following: the proposed method is predictive for ideal or nearly ideal mixtures; the correlation of mixtures of hydrocarbons having very different molar volumes can be obtained by optimizing only the binary interaction parameter linked to the enthalpic term; the new equation also correlates well with strongly non-ideal systems which exhibit a miscibility gap; the prediction of multicomponent vapor-liquid equilibria from the binary data alone is also reliable for both polar and non-polar mixtures.     

Association model of fluids. Phase equilibria in sulphur dioxide mixtures

The vapor-liquid and liquid-liquid equilibria of binary mixtures formed by sulphur dioxide with organic components are reproduced well using a new associated-solution model whose association and solvation constants are defined in terms of the modified segment fractions of chemical species. The model shows a good performance in predicting ternary vapor-liquid and liquid-liquid equilibria of sulphur dioxide mixtures from only binary parameters.     

Calculating binary and ternary multiphase equilibria: extensions of the integral area method

The area method was proposed in 1992 to calculate binary and ternary 2-phase equilibria. In its integral form, the method provides both the necessary and sufficient conditions required for the determination of the global minimum reduced Gibbs energy of mixing (Φ). The method has since been applied to the calculation of both pure component and ternary multiphase equilibria in a differential form. However, the extension of the original (2 point) integral area method to the direct calculation of both binary and ternary multiphase equilibria has not been completed. Direct 3 point and modified 2 point search methods have therefore been developed here and used to estimate the phase compositions of a representative binary vapour-liquid-liquid system. The 2 point area method principle has been extended and applied to the calculation of ternary multiphase equilibria using a net volume approach. However, this volume method was found to fail due to an underlying inconsistency in the bounding of the integrated Φ surface by the trial 3-phase region. A new method is proposed that overcomes this problem by minimising the area of intersection between a tangent plane and the Φ surface. This new method has successfully calculated the 3-phase compositions of two simple test systems from a variety of initial mixture starting points.