Capabilities and Limitations of Predictive Engineering Theories for

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Capabilities and Limitations of Predictive Engineering Theories for Multicomponent Adsorption Sofie Bartholdy,†,‡ Martin G. Bjørner,† Even Solbraa,§ Alexander Shapiro,† and Georgios M. Kontogeorgis*,† †

Center for Energy Resources Engineering (CERE), Department of Chemical and Biochemical Engineering, Technical University of Denmark, DK-2800 Lyngby, Denmark ‡ Haldor-Topsøe, Nymøllevej 55, DK-2800 Kgs. LyngbyDenmark § Statoil ASA, Research and Development Center, N-7005 Trondheim, Norway S Supporting Information *

ABSTRACT: Multicomponent adsorption of gas mixtures on diverse solid surfaces is important in many applications. However, there are still many questions on the practical applicability of the available theories, especially for polar systems. In this work, we consider three well-known theories suitable for the prediction of multicomponent adsorption with parameters obtained solely from correlating single gas/solid data. We have tested them over an extensive database with emphasis on polar systems (both gases and solids). The three theories are the multicomponent Langmuir, the ideal adsorbed solution theory (IAST), and the multicomponent potential adsorption theory (MPTA). We have not attempted to improve/modify the methods in any way but have used them in their original form, as the purpose of our work is to illustrate the capabilities and inherent limitations of the models for predicting multicomponent adsorption. We have ensured that the description of single gas/solid systems is as accurate as possible, but besides this, the calculations for multicomponent systems are straight predictions. The work revealed on one side that all three theories yield for some systems similar predictions, with IAST and MPTA performing overall better than the multicomponent Langmuir. On the other hand, it is also shown that all the three theories, despite the good results in some cases, have serious limitations particularly for water and to some extent also for certain polar solids. Both strengths and weaknesses of the three models are discussed.

1. INTRODUCTION AND MOTIVATION Most books in colloid and surface chemistry1−6 only discuss correlation of single component adsorption presenting a variety of theories such as Langmuir, Toth, Brunauer−Emmett−Teller (BET), etc. While adsorption from a single-component fluid (e.g., one gas or one liquid adsorbing on one solid) is, of course, of interest, multicomponent adsorption equilibria (e.g., a mixture of gases adsorbing on the same solid) are extremely important as well. There are many natural and engineering applications of multicomponent adsorption such as the design of heterogeneous chemical reactors, certain separations for removing low-concentration impurities and pollutants from fluid streams (e.g., dehydration of natural gas), as well as chromatography. In the natural gas example, the bulk phase consists of water, glycol, CO2, O2, N2, Ar, and light hydrocarbons, mostly methane, at pressures up to 200 bar. That combined with the fact that polar compounds are present makes the gas phase nonideal. To get a better understanding of the factors affecting this contamination and which parameter in the process can be changed to decrease the contamination, modeling of the multicomponent adsorption should be done, which in this case involves polar compounds. Adsorption is thus important to both reaction engineering and separation technology. However, despite its great importance, there are relatively few high quality data for multicomponent adsorption, compared to single component adsorption, especially for © 2013 American Chemical Society

polar mixtures. This is possibly one of the reasons why it is difficult to evaluate the performance of the existing theories. An additional complication is that solids are often very different (e.g., data reported on activated carbon or silica by different authors may actually refer to different solids). Due to these problems and the lack of many multicomponent data, the purpose of the theories should be to predict multicomponent adsorption based on single (gas) adsorption isotherm data. Many engineering theories for multicomponent adsorption can be roughly divided into three categories: extensions of the Langmuir equation, the thermodynamic approach (ideal and real adsorbed solution theories, IAST and RAST) ascribed to Myers and Prausnitz,7 and, finally, the potential adsorption theory, especially as pioneered to multicomponent systems by Shapiro and co-workers.8−12 There are other approaches that are very useful for multicomponent adsorption such as those based on SAFT theory,47,48 which have so far been used mostly for nonpolar gases. The purpose of this work is to evaluate the performance of the three aforementioned theories for the prediction of multicomponent gas adsorption on various solids. Emphasis is given on water and other polar gases and polar solids. Also, Received: Revised: Accepted: Published: 11552

February 24, 2013 July 11, 2013 July 20, 2013 July 22, 2013 dx.doi.org/10.1021/ie400593b | Ind. Eng. Chem. Res. 2013, 52, 11552−11563

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The thermodynamic theory for adsorption was first used in practical applications when Myers and Prausnitz7 proposed IAST, the ideal adsorbed solution theory, generalizing the earlier works by Lewis et al., de Boer, and others, starting from the first treatment by Gibbs. In the thermodynamic adsorption theory (see Figure 1), the adsorbed phase is a “black box”, that is, a homogeneous phase obeying common thermodynamic relations. An equation of state for this phase is obtained by analogy with a bulk phase or from experimental data. Thus, in the adsorbed solution theory, we follow a procedure known from thermodynamics in direct analogy to equations for vapor/liquid equilibria. We assume that there is thermodynamic equilibrium between the adsorbent (solid, a) and the adsorbate (gas) bulk phase:

we wish to emphasize that all models will be tested in the same predictive way; that is, single gas isotherms fitted to single gas/ solid adsorption data and all multicomponent results are predictions. The MPTA results have been recently reported.13 In this work, we focus on the detailed presentation of the results for IAST and multicomponent Langmuir and a comparative evaluation of all three theories.

2. THREE THEORIES FOR MULTICOMPONENT ADSORPTION Figure 1 gives a simplified physical picture of the three theories, which are hereafter briefly discussed.

μi = μi a

Pyi ϕi = P0i (π )γixi

(2)

In IAST, fugacity and activity coefficients shown in eq 2 are ignored, which makes the model predictive. In RAST (real adsorbed solution theory), activity coefficients should be used. Equation 2 is solved for the mole fraction of the gas in the solid, xi, at known values of T, P, and y. In eq 2, Pi0(π) is the pressure of pure gas i at the same spreading pressure as of the mixed adsorbate. This individual equilibrium pressure must be calculated for each component once the spreading pressure has been determined. The procedure is described in various textbooks and articles,7,8,16 and it will not be repeated here. It should be mentioned that single gas adsorption data or expressions for the single component adsorptions are needed in the process (e.g., the Langmuir or the three parameter Toth equation).22 Myers and Prausnitz7 mention that the pure component adsorption isotherms should be known very accurately at low surface coverage, because the integration for spreading pressure is sensitive to this part of the pure component adsorption isotherm. According to Smith et al.,16 no equation is known that leads to an adsorption isotherm, which, in general, fits experimental data over the entire concentration range up to full monolayer coverage. See a more detailed discussion in Shapiro and Stenby.14 An alternative approach to IAST/RAST, which combines a thermodynamic treatment with a specific consideration of fluid/solid interactions, is the potential theory of adsorption (Polanyi17 and Dubinin18,19), especially in the form designed for multicomponent mixtures proposed by Shapiro and Stenby.8 In the multicomponent potential theory of adsorption (MPTA), Figure 1, the adsorbate is considered to be an inhomogeneous phase. The surface of the adsorbent is supposed to be a source of a potential force f ield with the molecules being attracted to the surface by this field. The distribution of the fluid (gas, liquid) near the solid surface is given by the equilibrium conditions for segregation in the external potential field, with pressure and composition as the intensive variables that may vary with the distance. Consider adsorption on a surface from a gas phase with pressure P and mole fraction compositions in the gas phase y. Close to the surface, each component i of the gas mixture is affected by an adsorption potential εi(z) where z is the distance to the surface of the adsorbent. These potentials are not necessarily the same for all components; they may differ from one component to another due to different interaction forces with the surface.

Figure 1. Physical picture (from left to right) of the Langmuir, IAST (thermodynamic), and MPTA theories.

The Langmuir theory for multicomponent systems is an extension of the same well-known version of the theory for single gas/solid systems. The Langmuir equation is a conceptually and computationally simple model based on a (quasi) chemical picture of adsorption and a large number of rather drastic assumptions, especially that we have an “ideal” (clean, homogeneous, smooth, nonporous) surface that consists of a fixed amount of localized sites. Each site may either be free or occupied by an adsorbed molecule, and there are (almost) no lateral interactions between adsorbed molecules. Solute and solvent have the same size, and there is maximum creation of a single (mono)layer. For a more detailed discussion of the various extensions of the Langmuir equation, including the impact of heterogeneity, multiple layers, and different-size molecules, see the review by Shapiro and Stenby.14 Despite these drastic assumptions, the Langmuir approach is often also applied in areas where the assumptions behind it do not hold (e.g., adsorption of asphaltenes, surfactants, polymers, or proteins). The reason is that the Langmuir theory is the simplest model predicting a qualitatively correct behavior of the adsorbate in the two asymptotic limits: low coverage (linear adsorption) and high coverage (tending to saturation). For multicomponent systems, the Langmuir equation is written as ni biPi = Ns, i 1 + ∑i biPi

or

(1)

The summation is over all gases (or, in general, molecules) adsorbing on a solid. Ns is the total number of sites of the surface (approached at high pressures), and n is the number of occupied sites at a specified pressure. Both are expressed in the same unit (mol/g or similar (cm3/g or mol/m2)) while b, the equilibrium constant, is expressed in inversed pressure units (e.g., Pa−1). The parameters Ns and b are determined by fitting to experimental (e.g., single gas adsorption) data. In eq 1, the gas mixture obeys the ideal gas equation, and if not, the partial pressure Pi should be replaced by the fugacity. This has not been necessary in this work. 11553

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At equilibrium, we obtain the basic equation of MPTA by equating the chemical potentials in the external field as μi (z) − εi(z) = μgi

AADx is the % absolute average deviation for the mole factions and AADn is the % absolute average deviation for the amount adsorbed. The AADn is also determined for the isotherm fits. Mohammad et al.24 and Fitzgerald et al.25 discuss the experimental uncertainties of amounts adsorbed at equilibrium and conclude that they are 12% for constant pressure experiments. If the fixed volume method is used the uncertainty can be up to 42%, while the experimental uncertainties are estimated to be 5% for the total amount adsorbed. From these, we can conclude that a deviation of 5−10% from the experimental data should be considered to be a reasonably good result.

(3)

where z is distance from surface or porous volume and ε is the adsorption potential. Chemical potentials μi depend on z implicitly, in terms of pressure and molar fractions. Thus, given P and y in the gas bulk phase, the distributions of all the parameters (pressure and mole fractions) close to the surface are determined from eq 3. More details and the equations for the surface excess and adsorbed phase mole fractions are given by Shapiro and Stenby.8 The central idea of MPTA is that the chemical potential of a component in the mixture results from two contributions; a bulk-phase contribution for fluid/fluid interactions, which is represented by a thermodynamic model (equation of state) (e.g., SRK),20 and a potential energy contribution that depends on the distance between the gas component and the solid adsorbent (fluid/solid interactions). For the fluid/solid interactions, we need some expression for the potential that reflects the distribution of the components in the adsorbed phase. There are several such potential equations, and they typically contain 2 or 3 adjustable parameters, which are fitted to single gas adsorption data. Often used choices are the semiempirical Dubinin−Astakhov (DA) potential (Shapiro and Stenby8,21) or the well-known Dubinin−Radushkevich (DR) and Steele expressions. The three theories for multicomponent adsorption previously presented are fundamentally different, as they are based on the three different pictures of adsorption shown in Figure 1. Of the three theories, only MPTA accounts explicitly for fluid/ solid interactions via the potential function, while the others only account for that via the adjustable parameters. Nevertheless, there are some important similarities. All three theories (Langmuir, IAST, and MPTA) are predictive for multicomponent adsorption, thus permitting a fair comparison among them. The term “predictive” means that their parameters can be estimated from single-component adsorption isotherms. Moreover, all three theories rely (at least partially) on or incorporate thermodynamic aspects and/or can be related to concepts from bulk-phase thermodynamics. Moreover, IAST and Langmuir result in the same mathematical expressions under the assumption that the single-component adsorption isotherms (in IAST) may be approximated by the Langmuir expressions and both gases have the same maximum adsorption parameter. Computational aspects of the calculations with multicomponent Langmuir, IAST, and MPTA have been presented in the literature,8,23 and they will not be repeated here. We mention, however, that in this work all the deviations from experimental data are given as absolute average percentage deviations between experimental and calculated (predicted) values using the equations: 100 AADx = Nexp

AADn =

100 Nexp

3. LITERATURE STUDIES FOR PREDICTION OF MULTICOMPONENT ADSORPTION Langmuir vs IAST. Many applications of multicomponent Langmuir are in relation to the calculation of gas hydrate inhibition curves, where it is combined with the van der Waals−Platteeuw solid model (Kontogeorgis and Folas26). Several other applications of Langmuir have been reported. For example, Langmuir has been successfully applied for predicting the adsorption of liquid hydrocarbons on molecular sieves 5A, dry natural gas on activated carbon,27 on various adsorbents and simple gases on silica gel.28 In one of the few comparative studies in the literature, Chen et al.38 compared IAST to the multicomponent Langmuir equation (with fugacities) for the adsorption of gases at elevated pressures (15−25 bar). Multicomponent Langmuir was better than IAST for two binary gas mixtures (H2−CO and CO−CH4), but IAST was superior when modeling the systems CO−CO2 and CH4−CO2 and for all the ternary and quaternary systems considered. However, overall, both models proved to adequately predict the mixed gas data, and the predictions were very similar. Other comparisons between IAST and Langmuir have been presented for natural materials (ex. coal) in applications related to oil fields, for example, by Pan and Connell.50 IAST. IAST has been used extensively for predicting multicomponent adsorption, possibly as much as Langmuir and much more than MPTA (which is probably explained by the much longer history of the former model, which was de facto the only predictive multicomponent adsorption model in use during several decades). For a range of relatively simple mixtures containing hydrocarbons and CO2, O2, and N2, excellent results are obtained at various conditions (temperatures, various solids such as activated carbon and silica gel, selectivity, etc.), as shown first of all in the work of Myers and Prausnitz.7 It was shown, for example, that IAST can predict selectivity very well in some cases. For the system ethylene/CO2 on activated carbon, it is experimentally observed that ethylene is much more strongly adsorbed than CO2. On the same solid, ethane shows strong preferential adsorption over methane and both are very well represented by IAST, as shown by Myers and Prausnitz.7 Equally good results for the same type of gases on both activated carbon and molecular sieves have been presented by Sievers and Mersmann,29 Richter et al.,22 and Goetz et al.,30 verifying that IAST is a successful predictive model for these relatively simple systems. Despite these very promising results, there are serious problems reported by many authors, especially for polar gases and solids, for which relatively few studies are available. Li et al.31 studied the CO2/water adsorption on activated alumina, Perfetti and Wightman32 modeled with IAST the adsorption

Nexp

∑ |xi exp − xi calc| i=1

(4)

Nexp

∑ |(Nadsexp ,i − Nadscalc, i)/Nadsexp , i| i=1

(5) 11554



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Figure 2. Comparison of experimental data and calculated results for (left) acetone/benzene on MS-13X and (right) acetone/n-hexane on MS-13X.

porous coal49 and for adsorption from liquid solutions,10,11 even for systems exhibiting strongly “non-Langmuir” behavior. Summarizing the conclusions from literature studies, MPTA yields good results for the prediction of the adsorption of N2, methane, ethylene, and hydrocarbons on activated (and other) carbons as well as a few silica gel samples considered. Successful predictions at various temperatures were obtained as well for a few 4- and 5- component gas systems for which data are available on activated carbon. This is an important success of the theory, since the temperature dependence is only included into the bulk-phase equations of state, thus, unlike in IAST and Langmuir models, it is not fitted. The solid/fluid interaction potentials are assumed to be temperature-independent. In the majority of the cases, very good predictive results are obtained using one fitting parameter per substance and one common parameter (the adsorbent capacity). However, there may be need to use different adsorption capacities in the DR/DA potentials. The choice of the potential used for the fluid/solid interactions is very important.13 Another success of the model was its extension onto supercritical and nonmonotonous adsorption isotherms, where the two other models are inapplicable.12 In these investigations very few slightly polar systems were considered and the results were not very successful. It has been stated that very good densities are needed, which can be obtained if an advanced thermodynamic model (e.g., PCSAFT) is used instead of SRK (which is an often used choice). Moreover, unlike IAST (whose extension to liquid mixtures is rather complicated), MPTA can be readily extended to liquid mixtures with good results,11 especially when the Steele potential is used. It must be recalled, however, that the Steele potential has three adjustable parameters. Thus, it is unclear whether the improved performance is due to the better potential function or the additional (compared to the DA potential) adjustable parameter.

equilibrium of ethanol/benzene, ethanol/cyclohexane, and benzene/cyclohexane onto Graphon, and finally, Steffan and Akgerman33 considered the adsorption of diverse volatile organic compounds (hexane/benzene, hexane/trichloroethylene, chloroform/chlorobenzene) on silica gel. The common underlying conclusion from all of these studies is that IAST fails for water, ethanol, and even the slightly polar systems among those studied by Steffan and Akgerman.33 Thus, IAST does not appear to be a reliable model for polar systems. The reasons are not clear, but it could be because of the appreciable negative deviations from ideality observed due to differences in size of the adsorbate molecules and because of the adsorbent heterogeneity.16 Normally negative deviations from the molar “volumes” (surfaces) predicted by the IAST are observed in the experiments (contrary to bulk mixtures). This has led many authors to propose an extension of IAST, called real adsorbed solution theory (RAST) using nonunity activity coefficients (eq 2). The activity coefficients should be correlated from experimental data for the multicomponent system; thus, RAST is currently not a predictive model for multicomponent adsorption. Activity coefficients from “bulk-phase” thermodynamics are not appropriate for modeling the behavior of adsorbed phases.14 In RAST are needed activity coefficients, often less than unity, which are strong functions of both spreading pressure and temperature and sometimes asymmetric with respect to composition.34,35 These results are in contrast to activity coefficients for liquid phases which are, in the majority of cases, higher than unity (positive deviations) and insensitive to pressure. Thus, the activity coefficients from RAST should be considered not much more than fitting parameters, rather than the activity coefficients as we know them from bulk phase thermodynamics. This has been illustrated by many researchers (e.g., by Sochard et al.36). Myers postulated some years ago that reliable methods for the predictions of the activity coefficients needed in RAST may be discovered in the future.37 We do not think that this has been accomplished as yet. We are not aware of successful and, most importantly, predictive versions of the RAST approach. MPTA. MPTA is a highly successful model that in an effective way separates fluid/solid and fluid/fluid interactions. It can be used for prediction of multicomponent adsorption from single-component adsorption isotherms. It has been used8−12,21,39 both for the prediction of gas mixture adsorption on solids (including high pressures and supercritical conditions),9,12,21 adsorption of methane/CO2/N2 mixtures in

4. IAST VS LANGMUIRA SYSTEMATIC COMPARISON OF THE TWO THEORIES FOR MULTICOMPOMENT PREDICTIONS We have carried out an extensive comparison of IAST and multicomponent Langmuir over a wide range of adsorbates and adsorbents, including polar and hydrogen bonding ones. The systems considered comprised gas mixtures with various alcohols (methanol, ethanol, butanol, 2-propanol), acetone, water and several hydrocarbons on diverse adsorbents (activated carbon, silica and silica gel, molecular sieves, and a 11555



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Figure 3. Comparison of experimental data and calculated results for (left) methanol/n-hexane on MSC-5A and (right) methanol/benzene on MSC5A.

accounted for by the Langmuir model. IAST performs much better, for both methanol/acetone and methanol/benzene. Using the IAST+Toth combination, more accurate adsorbed amounts are obtained. On Molecular Sieving Carbon MSC-5A. A typical prediction result of the adsorption equilibrium on molecular sieving carbon 5A by IAST and multicomponent Langmuir is presented in Figure 3. The experimental data for methanol/n-hexane and acetone/ n-hexane are S-shaped, a trend that cannot be predicted by either IAST or Langmuir. The acetone/n-hexane system, however, shows evidence of hysteresis effects; that is, the Sshape may be due to experimental errors. For the system acetone/n-hexane, the multicomponent Langmuir gives the most accurate prediction although it underestimates the equilibrium at low concentration of acetone. IAST, on the other hand, overestimates the data over the entire mole fraction range. For methanol/acetone and methanol/ benzene the multicomponent Langmuir underestimates the selectivity of both systems, whereas IAST gives a reasonably good prediction, considering the scatter of data, especially for methanol/benzene (see Figure 3). For the system methanol/n-hexane the multicomponent Langmuir largely underestimates the selectivity, whereas IAST’s prediction is better in this system which shows an azeotropelike behavior. Methanol is an interesting case, as data are available and calculations are made in binary mixtures with n-hexane and benzene, respectively. Both are similar nonpolar solvents, with some tendency for benzene to solvate with methanol. The data show a different behavior that is partially captured by IAST but not at all by multicomponent Langmuir. The results summarized in Table S3 (Supporting Information) illustrate that for all methanol-containing systems, IAST +Toth is the best model (deviations within 10%), especially because of the better prediction of the adsorbed amount. On average, the deviation for all four systems is above 10% in all cases, mostly because of the poor performance for acetone/ hexane. 4.2. Activated Carbon G-2X. Konno et al.40 presented also experimental data for binary systems containing methanol and acetone on activated carbon G-2X at 303.15 K and 4 kPa. Table S4 (Supporting Information) shows the results with the Langmuir and Toth isotherms fitted to experimental (or extrapolated) data from the article. As expected, the Toth

zeolite). More than 200 different experimental data points were included in this evaluation. The multicomponent Langmuir was used in the form of eq 1 as using fugacities predicted by a thermodynamic model made little difference at the conditions of those systems. For IAST, the single gas adsorptions were correlated using either the Langmuir or Toth isotherms. The latter always correlates the single adsorption isotherms better, as it contains an additional adjustable parameter. We present a comparative evaluation of IAST and Langmuir divided first according to the adsorbents considered followed by an overall presentation. 4.1. Molecular Sieves. Konno et al.40 presented binary data for the adsorption of polar/nonpolar compounds on molecular sieve 13X (MS-13X) and molecular sieving carbon MSC-5A. As the actual data are not presented but correlations are given, we have back calculated the data based on these correlations. The experimental data, both pure gases and binaries, are obtained at 303.15 K and 4 kPa. The extrapolated data are fitted to the Langmuir and Toth isotherms with the parameters and accuracy presented in Table S1 (Supporting Information). Reasonably good fits are obtained in most cases, though as expected because of the additional parameter, the Toth isotherm provides a better correlation of the experimental data. The fitted parameters from Table S1 are used to predict the multicomponent (binary gas) data presented by Konno et al.40 The results are presented in Tables S2 and S3 (Supporting Information) and graphically, for characteristic systems, in Figures 2 and 3 in terms of the most polar compound in the mixture. We hereafter discuss the most important aspects from this study, first for MS-13X and then for MSC-5A. On Molecular Sieve MS-13X. One typical prediction of the adsorption equilibrium on molecular sieve 13X by IAST and multicomponent Langmuir is presented in Figure 2. It can be seen from Figure 2 that in both cases the multicomponent Langmuir model largely underestimates the selectivity. On the other hand, IAST predicts rather well the experimental data for the systems containing acetone and a nonpolar hydrocarbon. There is, however, no difference in the predictions of IAST using the Langmuir and the Toth isotherms. This may be due to similar fits (with Langmuir and Toth) at the pressure of the prediction 4 kPa. For the system methanol/acetone, the multicomponent Langmuir model is entirely unable to predict even the trend of the experimental data (predicts wrong selectivity), maybe due to strong competition of the adsorption sites, a phenomenon not 11556



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Figure 4. Comparison of experimental data and calculated results for (left) methanol/benzene on activated carbon G-2X and (right) methanol/nhexane on activated carbon G-2X.

Figure 5. Comparison of experimental data and calculated results by multicomponent Langmuir for 2-propanol/water on silica gel. (left) 5000 Pa; (right) 9960 Pa.

corresponding to a type IV isotherm according to Brunauer classification. Acceptable correlations at low pressures were obtained using the Toth and Langmuir isotherms. However, the IAST+Toth failed to produce any predictions due to the small range of common spreading pressures. IAST with the Langmuir parameters, on the other hand, was able to provide a solution and the IAST results as well as those of the multicomponent Langmuir are summarized in Table S6 (Supporting Information). From this and the graphical inspection, for example, in Figure 5, it is concluded that the multicomponent Langmuir model is unable to predict the selectivity over the entire concentration span. IAST+Langmuir predicts the adsorbed amount and the mole fractions somewhat closer to the data, but the deviations are very high in both cases. Moreover, these results when expressed in terms of standard deviations are rather deceptive because the trend for the experimental data is not predicted for the selectivity or the amount adsorbed. The data show a so-called azeotropic-like behavior (S-shaped selectivity plot), which appears to be impossible to predict by the IAST and multicomponent Langmuir models. 4.4. n-Heptane/Water on Silica Gel. Bering and Serpinskii42 presented experimental data for the adsorption equilibrium of n-heptane/water on silica gel at 348.15 K. As it was the case for the 2-propanol/water data on silica gel (discussed in section 4.3), the pure component isotherms are Sshaped. As before, we correlated the single gas adsorption isotherms with Langmuir and Toth, and successful results are

correlations are much better, due to the additional adjustable parameter. Using these parameters, multicomponent Langmuir and IAST are tested against the multicomponent data. The results are summarized in Table S5 (Supporting Information) and graphically for a characteristic system in Figure 4. It can be seen that the multicomponent Langmuir gives the best predictions for acetone/benzene, methanol/hexane, and methanol/benzene. IAST+Langmuir performs, surprisingly, better than IAST +Toth, but both underestimate the selectivity (for the acetone and methanol-containing systems). A slightly different picture is observed for methanol/acetone. Here IAST+Langmuir is the best model of all, although the predictions are quite similar. It should be noted, however, that for the prediction of the adsorbed amounts all models fail to reproduce the trends of the experimental data at high mole fractions of methanol due to significant enhanced adsorption, which no model predicts. The same gases were studied (and measured by same authors) also on molecular sieves 13X and molecular sieving carbon 5A, as shown in section 4.1. By comparing the results, we see a better performance of all models on activated carbon G-2X, where several deviations are less than 10%. 4.3. 2-Propanol/Water on Silica Gel. Wolf and Schlunder41 presented experimental data for the adsorption equilibrium of 2-propanol and water on silica gels at 288.15 and 333.15 K and pressures below 35 kPa (mostly in the gas region). All the pure component isotherms are S-shaped curves 11557



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Figure 6. Experimental data and prediction with IAST and multicomponent Langmuir for ethanol-benzene on Cab-O-sil at 293.15 K.

Table 1. Percentage Absolute Average Deviations (% AAD) between Predicted Results and Experimental Data for the Adsorption Isotherms (x) and Total Amounts Adsorbed (n) Using the Multicomponent Langmuir and IAST Modelsa adsorbates

adsorbentc

NS/NPb

IAST−Langmuir (%x/%n)

IAST−Toth (%x/%n)

multicomponent Langmuir (%x/%n)

methanol, acetone, benzene, hexane methanol, acetone, benzene, hexane methanol, acetone, benzene, hexane 2-propanol/water heptane/water ethanol, benzene, cyclohexane ethanol, benzene, cyclohexane total/avg

MS-13X MS-carbon 5A AC G-2X silica gel silica gel Cab-o-sil (293 K) Cab-o-sil (303 K)

4/25 4/41 5/32 2/10 2/6 3/25 6/52 26/191

11/21 17/13 13/6 10/23 14/26 6/33 5/42 11/23

13/16 18/11 16/9

51/38 21/17 9/9 19/49 15/26 4/32 5/41 18/30

15/26 4/26 7/41 12/22

a The first value is the % AAD in x and the second is the % AAD in n. bNS = number of systems; NP = number of data points. cMS = molecular sieve; AC = activated carbon.

benzene, 3.6 kPa for ethanol/cyclohexane, and 3.8 kPa for benzene/cyclohexane). Both IAST and multicomponent Langmuir predict the selectivity quite accurately (less than 10% deviation), even though both models fail in predicting the adsorbed amounts at equilibrium. There are some uncertainties in the experimental data, but it seems also that the model does not even predict the trend of the experimental data points. It should be noted that the experimental data for benzene/cyclohexane indicate the presence of an azeotrope-like behavior at high mole fraction of benzene, which cannot be predicted by the models. Moreover, none of the models were able to predict the adsorbed amount with good accuracy. The deviations are in all cases above 25%. Multicomponent Langmuir and IAST produce very similar results for all systems adsorbing on Cab-O-Sil. Both models predict the selectivity between the components with good accuracy (below 6%) in all cases. The adsorbed amount is predicted less satisfactorily, although there may be uncertainties on these experimental measurements. In addition to the systems presented in sections 4.1−4.5, we have considered the adsorption of 1-butanol/xylene on a zeolite and water/hydrocarbon adsorption on two different activated carbons. The data were from Takeuchi et al.45 and Okazaki et al.46 None of the models could provide satisfactory solutions that are worth reporting for these systems, and thus, they are not discussed further. 4.6. Summary of the Results with IAST and Multicomponent Langmuir Model. Table 1 presents an overview of the main results for those systems for which calculations were possible. The scatter encountered in several experimental data for multicomponent adsorption should be considered

obtained even at low pressures. Tables S7 and S8 (Supporting Information) summarize the binary and the multicomponent results. It has been possible to obtain a solution with both IAST +Langmuir and IAST+Toth for the multicomponent system. All models, including multicomponent Langmuir, perform identically and not very satisfactorily, with deviations around 14% for the mole fraction and over 25% for the absorbed amount. The model captures the curvature to some extent (although it is difficult to say with only three experimental points), and as usual, the models perform better for the selectivities than for the adsorbed amounts. 4.5. Binary Adsorption on Cab-O-Silica. Experimental data for the adsorption equilibrium of mixtures in Cab-O-Sil, which is a flame hydrolyzed silica, are presented in two works by Perfetti and Wightman43,44 at 293.15 K and at 303.15 K. The data are for the adsorption equilibrium of the systems ethanol/benzene, ethanol/cyclohexane, and benzene/cyclohexane at 293.15 K and 4 kPa and for the same systems at 303.15 K and varying pressures (3−6 kPa). The correlations of the pure gas isotherms using the Langmuir and Toth models are shown in Tables S9 and S10 (Supporting Information). The results for the multicompoment adsorption are summarized in Tables S11 and S12 (Supporting Information), while a typical example is shown graphically in Figure 6. Notice that for the systems containing ethanol it was impossible to produce a solution with the IAST using the Toth isotherm because no common spreading pressure was found. Moreover, at the higher temperature, the total pressure is not constant for the binary adsorption data, so that an average pressure had to be used in the simulations (3.4 kPa for ethanol/ 11558



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when evaluating the performance of the models. There are several cases where the results are “surprising” or difficult to explain. This may be due to the data quality, because of the presence of interactions between adsorbates, or different competitions for the adsorption sites, which are not considered, or, finally, due to the effect of the heterogeneity of the adsorbent and possible capillary condensation effects. As an example of these surprising results, we can mention the adsorption on molecular sieving carbon with IAST+Langmuir. The performance is very good for methanol/hexane and for methanol/acetone, but not for acetone/hexane. There is no immediate explanation for this behavior. Nevertheless, some general trends do exist and a few conclusions can be made. None of the approaches perform very satisfactorily in all cases and actually overall IAST and multicomponent Langmuir perform similarly, with IAST being somewhat better. Even though the differences on percentage deviations are similar and small for some systems, IAST performs overall better than the multicomponent Langmuir, with the latter being completely off for some systems (e.g., for adsorption on molecular sieves). On the other hand, both theories have problems for most polar gases and solids, especially for water and silica gel systems. For both 2-propanol/water and heptane/water, even though the percentage deviations do not seem that high, especially with IAST, the results are deceptive because the trends of the experimental data with respect to selectivity or the amount adsorbed are not predicted well at all! Water and very polar solids (zeolite, silica gel) present problems in almost all cases. This is, however, not a general conclusion for all polar gases. The adsorption of many alcohols on several solids is predicted as well as the adsorption of the nonpolar hydrocarbons, see, for example, the results in Tables S11 and S12 (Supporting Information). On a more detailed level, it is observed that, in agreement to previous studies and what could be expected, the models perform worse for the prediction of the total amounts adsorbed than for the selectivity and composition of the adsorbate (with the error almost doubled in the former case). As expected, none of the models can predict well those cases with S-shape adsorption curves (e.g., acetone/hexane and methanol/hexane) in MS-Carbon-5A. Finally, somewhat in contradiction to other studies, using a “better” theory for correlating the single gas adsorption isotherms did not improve the predictions for the multicomponent systems. Actually, the results of IAST using either Langmuir or Toth are overall very similar. There are even some cases where IAST+Langmuir perform better than IAST+Toth. This is surprising since the Toth model correlates in all cases better the single gas adsorption isotherms. However, the Toth equation is an effective three-parameter fitting isotherm that is not fully theoretically justified, and this is a possible explanation for the less satisfactory results for the multicomponent systems. We can thus conclude that, despite its positive characteristics, there are several cases where the results with IAST, even the good ones, are due to cancellations of errors for multicomponent systems.

binary gas systems (more than 600 points) on activated carbon, molecular sieves, silicates, and silica gels as well as 8 ternary gas systems with about 120 data points on the same type of solids. It should be noticed that all the individual adsorption isotherms were modeled by the Toth equation for IAST and that the cases of strongly non-Langmuir behavior, where MPTA is clearly better, were not considered in their work. Monsalvo and Shapiro reported results both in terms of adsorption equilibria (mole fractions, x) and, when available, also for total adsorbed amounts (n). For the binary systems, the % deviation with MPTA is 5 and 9 (over the whole database, respectively for x,n) and 5 and 7 for IAST (x,n). For the ternary gas systems, the deviations are higher but nevertheless similar with the two approaches (around 11−12 for both MPTA and IAST; here the differences in the model performance for adsorption equilibria and total adsorbed amounts is smaller than for binary gas systems). The authors conclude that both IAST and MPTA are able to predict binary and ternary gas adsorption with the right trends and good accuracy. There are problems in some cases, such as for mixtures exhibiting azeotrope-like behavior such as CO2−H2S and CO2−C3H8. It is worth mentioning that (considering also that the Toth equation was used in the IAST case) MPTA employs fewer parameters in the correlation of the single component adsorption data. An extensive investigation on MPTA has been carried out by Bjørner et al.13 using a database similar to the one employed in this work. An overview presentation of these results, also compared to the results with IAST and multicomponent Langmuir shown here, is shown in Table 2. Bjørner et al.13 used MPTA with two equations of state, but in Table 2, we show results only for the MPTA+SRK combination. Moreover, in order to improve the results but also have a more fair (in terms of number of adjustable parameters) comparison to IAST, Bjørner et al.13 considered

5. DISCUSSIONA COMPARISON OF THREE PREDICTIVE THEORIES Monsalvo and Shapiro9 carried out an extensive comparison of MPTA (using two different equations of state for the fluid/fluid interactions) and IAST. They considered the adsorption of 40

The first value is the % AAD in x and the second is the % AAD in n. Compiled based on the results from Bjørner et al.13 “Common” indicates using a common capacity z; “Individual” indicates using an individual capacity z. bAverage calculated with IAST and multicomponent Langmuir for the same systems as those tested with MPTA.

Table 2. % AAD between Predicted Results and Experimental Data for the Adsorption Isotherms (x) and Total Amounts Adsorbed (n) Using MPTA with the SRK Equation of Statea adsorbates

NS/ NP

MPTA + SRK common

MPTA + SRK individual

MS-13X

4/25

21/19

22/18

MS-carbon 5A

4/41

24/15

16/12

AC G-2X

5/32

16/10

7/6

Cab-o-sil (293 K) Cab-o-sil (303 K)

3/25

8/35

8/37

6/25

4/23

4/21

15/20

11/19

adsorbent

methanol, acetone, benzene, hexane methanol, acetone, benzene, hexane methanol, acetone, benzene, hexane ethanol, benzene, cyclohexane ethanol, benzene, cyclohexane total/avg avgb IAST−Langmuir IAST−Toth multic. Langmuir

10/23 12/21 18/27

a

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IAST with Langmuir rather than with Toth. There are also issues with MPTA. One would expect that using individual capacities (where the number of adjustable parameters is almost doubled) would lead to more flexibility and best results for all systems, but there are several cases where this plays no difference or where even using common capacity performs best. Overall, there is an improvement in MPTA results of 2−3% using individual capacities.13 It appears that the common capacity assumption is valid only for similar molecules, and individual capacities should be used at least for nonlike molecules, one example being methanol and n-heptane. As can be understood, there is no “single winner model” and there are many issues to consider with all approaches, which complicates the situation. Nevertheless, we could state that MPTA and IAST perform overall similarly while multicomponent Langmuir is clearly the worst model of the three. The similarity in the results between IAST and MPTA is not entirely surprising. As Shapiro and Stenby have shown, IAST is consistent with the potential theory if the bulk phase is an ideal gas mixture for all the pressures arising under the action of the potential field of the adsorbent.8 This may be the case of lowpressure adsorption and if the adsorption potentials are rather weak in the adsorbate volume. However, the adsorption potentials are usually very strong close to the surface, where effective pressures of hundreds and thousands of MPa are developed. In the aforementioned discussion, as said previously, MPTA +SRK results from Bjørner et al.13 are considered. Overall, it makes little difference if MPTA+CPA is used. The CPA (Kontogeorgis et al.15) was the other thermodynamic model combined with MPTA in the work of Bjørner et al.13 There is a minor change in the performance for adsorption on Cab-O-Sil, while there are changes for the three other solids. In the case of MS-13X, MPTA+CPA turns out to be among the winner models for methanol with acetone and benzene and for acetone/hexane and for MS-5A also for methanol/acetone. Unfortunately, MPTA+CPA performs worse than MPTA+SRK and changes status from “winner” to “loser” for adsorption of methanol/benzene and acetone/hexane on MS-5A and for adsorption of three systems (methanol with hexane, benzene and acetone/benzene) on G-2X. Thus, we have 4 new “winner” and 5 new “loser” systems for MPTA+CPA vs MPTA+SRK. As Bjørner et al.13 report, the predictions with MPTA are of the order 7−12% with the best performing equation of state. While this result is comparable to previously reported results with MPTA for nonpolar systems, we do not know a priori which thermodynamic model performs best in combination with MPTA. The polarity of adsorbents offers some indication for the selection of the best thermodynamic model to be used in MPTA.13 Among the adsorbents studied here, MS-5A and ACG2X are nonpolar, MS-13X and SG/SGCC are polar, and CabO-Sil has an intermediate polarity. MPTA+SRK performs best for associating/nonassociating mixtures on nonpolar/slightly polar solids and MPTA+CPA is the best model for polar adsorbents and two associating compounds. These recommendations, however, cannot be final due to the limited database used. All of these conclusions, as discussed by Bjørner et al.,13 illustrate that much more is needed for improving the results with MPTA than simply changing to a possibly better/moresuitable-for-complex-systems thermodynamic model. Clearly, there are other factors that play an important role.

both common and individual capacities for the adsorbents in the various systems. As seen from Table 2, comparing also the results to those of the other models, overall MPTA performs as accurately as IAST+Langmuir and better than the multicomponent Langmuir. The investigation of Bjørner et al.13 showed that using more advanced equations of state than SRK do not always lead to better adsorption results, thus further investigation on the MPTA model is needed, especially for complex systems (adsorbates and adsorbents). This is briefly discussed later. Another way to compare the results of MPTA (from Bjørner et al.13) to those from this work is to study them per system or for the four adsorbents (MS13-X, 5A, G-2X, and S) considered in both works. In our statements, we take into account the overall performance of the models for both the selectivities and the adsorbed amounts. For MS-13X, four systems are considered (methanol/ acetone, methanol/benzene, acetone/hexane, and acetone/ benzene). For this solid, IAST performs best for the two methanol systems, and all models (except for Langmuir) perform equally well for acetone/hexane, whereas MPTA (with common capacity) performs best for acetone/benzene. For MS-5A, the first three systems studied are the same as for MS13X, but instead of acetone/benzene, methanol/hexane is considered. In this case, IAST performs best for methanol/ hexane, while all models (except for Langmuir) are equally good for methanol/benzene. For the acetone/MS-5A systems, we observe that MPTA and Langmuir are best for acetone/ hexane, but IAST and MPTA (single capacity) perform best for methanol/acetone. For G-2X, five systems are considered (methanol with acetone, hexane, and benzene and acetone with hexane and benzene). MPTA (especially when individual capacities are used) is overwhelming the best model here in all cases except for methanol/acetone where IAST performs best. IAST performs equally well as MPTA for the methanol/benzene system as well, while multicomponent Langmuir performs equally well as MPTA for acetone/benzene. Finally, for S (Cab-O-Sil), three systems (ethanol/benzene, ethanol/cyclohexane, and benzene/cyclohexane) were studied at two different temperatures. At the low temperature, MPTA is the best model for all three systems (IAST being equally good for the nonpolar mixture), while at the higher temperature all models perform equally well. However, the Toth equation cannot be reliably used within IAST for these systems. So, how many “winners” do we have per model for all commonly studied 19 systems? With the rather simplified term “winner” we indicate the best performing models. The answer is IAST, 12; MPTA, 13; Langmuir, 5. In the results shown, if equally good performance is noted, more than 1 “winner model” is nominated. There are several aspects to be mentioned here. Not all “winner” models provide an excellent description for the multicomponent adsorption. Usually, the selectivity (%AAD in mole fractions) for the best models will be less than 10%, but the deviations in the adsorbed amount can be 15−30% even in the best case scenario (winner models). The second aspect is for IAST where there may be an effect of the model used for describing the single gas isotherms. While the Toth model is clearly the best for correlating the single gas/solid systems, for the multicomponent systems, it makes often no difference, not to say that in some cases it may be more reliable to combine 11560



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equation is, in its single adsorption form, in combination with the thermodynamic approaches of IAST and RAST. IAST is a popular approach, especially because of its apparent simplicity (although there are some hidden problems in simulations) and similarity to bulk-phase thermodynamics. From a fundamental point of view, IAST is a model that attempts to describe adsorption looking, in a simplified way, only at its thermodynamic aspects and ignoring the molecular interactions in the adsorbed solid layer solid. Nevertheless, when IAST works well, for example, for relatively simple gas mixtures, then we have an excellent predictive model for multicomponent adsorption. According to the literature single gas adsorption isotherms needed in IAST should be modeled with exceptional accuracy, but we found little justification for this in our work where both Langmuir and Toth perform equally well when combined with IAST for predicting multicomponent adsorption. As often negative deviations are observed in solid/gas systems, activity coefficients are needed. In this way, the RAST can be used, but the resulting model is not predictive anymore for multicomponent adsorption; thus, it is of rather limited applicability for engineering applications. MPTA is developed as an alternative to the ”Langmuir” and ”thermodynamic” type approaches, but it also resembles a simplified version of the full DFT theory. MPTA with the concept of surface potentials provides more physical information about adsorption equilibria than the purely thermodynamic approach. Similar to IAST, MPTA is predictive for gas mixtures (as the parameters are obtained from pure gas adsorption data). MPTA typically uses fewer or the same number of adjustable parameters as IAST. Especially when considering that for single gas adsorption data available at various temperatures, MPTA correlations are being conducted using all data; thus, the MPTA potential is considered to be temperature independent (although this may not be the case for polar compounds). An additional positive feature about MPTA is that it is the only one of the three models that can be and has been generalized onto several complex cases such as liquid solutions, supercritical/high pressure, and non-Langmuir adsorption behavior. Our work has resulted to several conclusions on the performance of the three adsorption theories for gas adsorption on diverse solids. We have used an extensive database including several polar gases and adsorbents. All models have been treated equally and used for predictions. This means that the results shown in this work for binary gas mixtures are all predictions using parameters obtained solely from single gas adsorption data. The main conclusion is that all three models evaluated can be used with diverse degrees of success for predicting multicomponent adsorption. Of the three models evaluated, Langmuir is overall the least successful one. In almost all cases and with all theories, we get much better predictions of the selectivities than for the adsorbed amounts. MPTA and IAST give overall similar results for multicomponent gas adsorption. There are positive features with all models, especially MPTA and IAST, but it is difficult to conclude a priori which model will perform best for which system. All theories have problems for some systems, especially for polar/hydrogen bonding adsorbates and complex solids such as water-containing systems and silica solids.

Based on these results and discussions, we are now ready to discuss what is possible and what is not for predicting multicomponent adsorption. Our investigation shows that much is indeed possible. For example, we can state that we do have theories that can predict multicomponent adsorption of gases on diverse adsorbents based alone on single gas isotherm data. We can also state that IAST and MPTA are equally predictive and with equally good results. The results are not the same for the various systems, and actually, it is not easy a priori to predict which theory performs best for which system, but overall, the results are similar. We can also state with equal certainty that multicomponent Langmuir is clearly the worst model among the three and could be eliminated from further studies. There are also many issues that are not clear or not possible. It is not possible a priori to point out a winner model. We cannot get for polar gases/solids the same good performance with IAST and MPTA as that reported previously in the literature for hydrocarbons/CO2/N2 and similar compounds adsorbing on activated carbon and similar solids. We cannot always obtain good results even with the best models. While 10% deviation in selectivities is possible in many cases, this is not the case with the adsorbed amounts where 20% deviations are typical. The amount of multicomponent data is not overwhelming neither is always their quality; thus, several of the conclusions can be partially affected by the type, nature, and quality of available data. For water adsorption almost in all cases, we have serious problems. There are no “apparent” solutions to these problems. IAST cannot be improved furtherimprovement means using RAST or similar models with extra parameters rendering these approaches nonpredictive for multicomponent systems. Similarly for MPTA, it was hoped that a solution could be a more advanced model for the fluid/fluid interactions, but it turned out that the problem is more complex and fluid/solid interactions may play a more important role.13 Relevant research has been carried out by Monsalvo and Shapiro,11,12 but more advancements are required in this direction. Our study points out that fundamental improvements for all approaches are needed, at least for predicting multicomponent adsorption of polar systems.

6. CONCLUDING REMARKS Three theories for multicomponent adsorption have been presented, the extension of Langmuir’s theory to multicomponent systems, the ideal and real adsorbed solution theories (IAST, RAST) and the multicomponent potential adsorption theory (MPTA). All theories have strengths and weaknesses. To our knowledge, there have not been many systematic comparisons of the performance of the various theories over a large number of polar experimental multicomponent adsorption data. No large databases or adsorption models parameter databases for any of these theories are available that also include polar/ associating mixtures. This work and the recent one by Bjørner et al.13 present two of the few systematic investigations of all three theories over an extensive database. The advantage of Langmuir’s approach for multicomponent systems is its simplicity and often good performance for relatively simple systems. Addition of new physical mechanisms to improve the model and relax some of its assumptions has resulted to cumbersome equations, which have not found widespread use. An alternative way to use the Langmuir 11561



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(16) Smith, J. M.; Van Ness, H.; Abbott, M. Introduction to Chemical Engineering Thermodynamics; McGraw-Hill Education: New York, 2001. (17) Polanyi, M. Ü ber die Adsorption vom Standpunkt des dritten Wärmesatzes. Verb. Dtsch. Phys. Ges. 1914, 16, 1012. (18) Dubinin, M. M.; Zaverina, E. D. Zh. Fiz. Khim. 1949, 23, 469. (19) Dubinin, M. M.; Zaverina, E. D.; Radushkevich, L. V. Zh. Fiz. Khim. 1947, 21, 1351. (20) Soave, G. Equilibrium Constants from a Modified Redlich− Kwong Equation of State. Chem. Eng. Sci. 1972, 27, 1197. (21) Dundar, E.; Zacharia, R.; Chahine, R.; Bénard, P. Modified Potential Theory for Modeling Supercritical Gas Adsorption. Int. J. Hydrogen Energy 2012, 37, 9137. (22) Richter, E.; Schotz, W.; Myers, A. L. Effect of Adsorption Equation on Prediction of Multicomponent Adsorption Equilibria by the Ideal Adsorbed Solution Theory. Chem. Eng. Sci. 1989, 44, 1609. (23) Valenzuela, D. P.; Myers, A. L. Adsorption Equilibrium Data Handbook; Prentice Hall: Upper Saddle River, NJ, 1989. (24) Mohammad, S.; Fitzgerald, J.; Robinson, R. L.; Gasem, K. A. M. Experimental Uncertainties in Volumetric Methods for Measuring Equilibrium Adsorption. Energy Fuels 2009, 23, 2810. (25) Fitzgerald, J. E.; Pan, Z.; Sudibandriyo, M.; Robinson, R. L., Jr.; Gasem, K. A. M.; Reeves, S. Adsorption of Methane, Nitrogen, Carbon Dioxide and their Mixtures on Wet Tiffany Coal. Fuel 2005, 84, 2351. (26) Kontogeorgis, G.; Folas, G. Thermodynamic Models for Industrial Applications: From Classical and Advanced Mixing Rules to Association Theories; John Wiley & Sons: New York, 2010. (27) Bazan, R. E.; Bastos-Neto, M.; Staudt, R.; Papp, H.; Azevedo, D. C. S.; Cavalcante, C. L., Jr. Adsorption Equilibria of Natural Gas Components on Activated Carbon: Pure and Mixed Gas Isotherms. Adsorpt. Sci. Technol. 2008, 26, 323. (28) Kapoor, A.; Ritter, J. A.; Yang, R. T. Extended Langmuir Model for Adsorption of Gas Mixtures on Heterogeneous Surfaces. Langmuir 1990, 6, 660. (29) Sievers, W.; Mersmann, A. Correlation of Single and Prediction of Multicomponent Adsorption Equilibria at High Pore Filling Degrees. Stud. Surf. Sci. Catal. 1994, 87, 99−108. (30) Goetz, V.; Pupier, O.; Guillot, A. Carbon Dioxide−Methane Mixture Adsorption on Activated Carbon. Adsorption 2006, 12, 55. (31) Li, G.; Xiao, P.; Webley, P. Binary Adsorption Equilibrium of Carbon Dioxide and Water Vapor on Activated Alumina. Langmuir 2009, 25, 10666. (32) Perfetti, G. A.; Wightman, J. P. Adsorption of Mixed Vapors on Solids. I. Graphon. Carbon 1975, 13, 473. (33) Steffan, D. G.; Akgerman, A. Multicomponent Adsorption Equilibria of Some Volatile Organic Compounds in the Presence of Water at Temperatures Below Their Normal Boiling Point. Environ. Eng. Sci. 1998, 15, 191. (34) Myers, A. L. Activity Coefficients of Mixtures Adsorbed on Heterogeneous Surfaces. AIChE J. 1983, 29, 691. (35) Talu, O.; Li, J.; Myers, A. L. Activity Coefficients of Adsorbed Mixtures. Adsorption 1995, 1, 103. (36) Sochard, S.; Fernandes, N.; Reneaume, J. Modeling of Adsorption Isotherm of a Binary Mixture with Real Adsorbed Solution Theory and Nonrandom Two-Liquid Model. AIChE J. 2010, 56, 3109. (37) Myers, A. L. Thermodynamics of Adsorption. In Chemical Thermodynamics for Industry ; Letcher, T. M., Ed.; Royal Society of Chemistry: Cambridge, UK, 2004; pp 243−253. (38) Chen, Y. D.; Ritter, J. A.; Yang, R. T. Nonideal Adsorption from Multicomponent Gas Mixtures at Elevated Pressures on a 5A Molecular Sieve. Chem. Eng. Sci. 1990, 45, 2877. (39) Shojaei, H.; Jessen, K. Application of Potential Theory to Modeling of ECBM Recovery. SPE Western North American Region Meeting, Anchorage, AK, 2011; Paper No. SPE144612, DOI: 10.2118/ 144612-MS. (40) Konno, M.; Terabayashi, M.; Takako, Y. Adsorption Equilibria of Hydrocrabon Gaseous Mixtures Containing Polar Components. J. Chem. Eng. Jpn. 1985, 18, 398.

We consider this work and the recently published one by Bjørner et al.13 as the first steps toward a systematic evaluation of predictive theories for multicomponent adsorption. We believe that definite conclusions can only be reached via a more complete evaluation of the models based on a very extensive database of well-selected and checked experimental multicomponent adsorption data. Nevertheless, we also believe that all theories, even the rather successful IAST and MPTA, require serious improvements for predicting the adsorption of polar systems (gases, adsorbents). These improvements should be done in a way that retains the predictive character of the models for multicomponent systems so that they can continue to be useful for industrial applications.

■

ASSOCIATED CONTENT

S Supporting Information *

Tables with parameters of the various models fitted to binary adsorption data and results for the predictions of multicomponent adsorption systems. This information is available free of charge via the Internet at http://pubs.acs.org

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Hiemenz, P. C.; Rajagopalan, R. Principles of Colloid and Surface Chemistry, Third ed., Revised and Expanded; Taylor & Francis: New York, 1997. (2) Barnes, G. T.; Gentle, I. R. Interfacial Science: An Introduction; Oxford University Press: Oxford, 2005. (3) Shaw, D. J. Introduction to Colloid and Surface Chemistry, 4th ed.; Butterworth-Heinemann: Oxford, 1992. (4) Hunter, R. J. Introduction to Modern Colloid Science; Oxford Science: Oxford, 1993. (5) Hamley, I. W. Introduction to Soft Matter: Polymers, Colloids Amphiphiles, and Liquid Crystals; Wiley: New York, 2000. (6) Pashley, R. M.; Karaman, M. E. Applied Colloid and Surface Chemistry; Wiley, 2004. (7) Myers, A. L.; Prausnitz, J. M. Thermodynamics of Mixed-Gas Adsorption. AIChE J. 1965, 11, 121. (8) Shapiro, A. A.; Stenby, E. H. Potential Theory of Multicomponent Adsorption. J. Colloid Interface Sci. 1998, 201, 146. (9) Monsalvo, M. A.; Shapiro, A. A. Modeling Adsorption of Binary and Ternary Mixtures on Microporous Media. Fluid Phase Equilib. 2007, 254, 91. (10) Monsalvo, M. A.; Shapiro, A. A. Prediction of Adsorption from Liquid Mixtures in Microporous Media by the Potential Theory. Fluid Phase Equilib. 2007, 261, 292. (11) Monsalvo, M. A.; Shapiro, A. A. Modeling Adsorption of Liquid Mixtures on Porous Materials. J. Colloid Interface Sci. 2009, 333, 310. (12) Monsalvo, M. A.; Shapiro, A. A. Study of High-Pressure Adsorption from Supercritical Fluids by the Potential Theory. Fluid Phase Equilib. 2009, 283, 56. (13) Bjørner, M. G.; Shapiro, A. A.; Kontogeorgis, G. M. Potential Theory of Adsorption for Associating Mixtures: Possibilities and Limitations. Ind. Eng. Chem. Res. 2013, 52, 2672. (14) Shapiro, A. A.; Stenby, E. H. Multicomponent Adsorption: Principles and Models. In Adsorption: Theory, Modeling, And Analysis; Toth, J., Ed.; Marcel Dekker: New York, 2002. (15) Kontogeorgis, G. M.; Voutsas, E. C.; Yakoumis, I. V.; Tassios, D. P. An Equation of State for Associating Fluids. Ind. Eng. Chem. Res. 1996, 35, 4310. 11562



Article

(41) Wolf, H. E.; Schlünder, E. U. Adsorption Equilibria of Solvent Mixtures on Silica Gel and Silica Gel Coated Ceramics. Chem. Eng. Process. 1999, 38, 211. (42) Bering, B. P.; Serpinskii, V. V. Adsorption of a Mixture of Gases. Russ. Chem. Bull. 1961, 10, 1817. (43) Perfetti, G. A.; Wightman, J. P. Adsorption from Binary Vapor Mixtures onto Cab-O-Sil. J. Colloid Interface Sci. 1974, 49, 313. (44) Perfetti, G. A.; Wightman, J. P. Adsorption of Mixed Vapors on Solids. II. Cab-O-Sil. J. Colloid Interface Sci. 1976, 55, 252. (45) Takeuchi, Y.; lwamoto, H.; Miyata, N.; Asano, S.; Harada, M. Adsorption of 1-Butanol and p-Xylene Vapor and Their Mixtures with High Silica Zeolites. Sep. Technol. 1995, 5, 23. (46) Okazaki, M.; Tamon, H.; Toei, R. Prediction of Binary Adsorption Equilibria of Solvent and Water Vapor on Activated Carbon. J. Chem. Eng. Jpn. 1978, 11, 209. (47) Martinez, A.; Castro, M.; McCabe, C.; Gil-Villegas, A. Predicting Adsorption Isotherms using a Two-Dimensional Statistical Associating Fluid Theory. J. Chem. Phys. 2007, 126, 074707. (48) Castro, M.; Martinez, A.; Gil-Villegas, A. Modelling Adsorption Isotherms of Binary Mixtures of Carbon Dioxide, Methane, and Nitrogen. Adsorp. Sci. Technol. 2011, 29, 59. (49) Shojaei, H.; Jessen, K. Application of Potential Theory to Modeling of ECBM Recovery. SPE 144612, 1. (50) Pan, Z.; Connell, L. D. Comparison of Adsorption Models in Reservoir Simulation of Enhanced Coalbed Methane Recovery and CO2 Sequestration in Coal. Int. J. Greenhouse Control 2009, 3, 77.

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