Using Local IAST with Micropore Size Distribution To Predict

Nov 12, 1999 - The MPSD−IAST model predictions are examined with the equilibrium data of mixed gases measured on two commercial activated carbons (A...
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Using Local IAST with Micropore Size Distribution To Predict Multicomponent Adsorption Equilibrium of Gases in Activated Carbon Shizhang Qiao, Kean Wang, and Xijun Hu* Department of Chemical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong Received June 17, 1999. In Final Form: September 23, 1999 A mathematical model is proposed to predict multicomponent adsorption equilibrium of gases in a heterogeneous activated carbon. The model, called MPSD-IAST, assumes a micropore size distribution (MPSD) to represent the energetic heterogeneity of adsorbent and uses the ideal adsorbed solution theory (IAST) to describe the local multicomponent adsorption equilibrium within a given pore. The overall adsorption isotherm is the integral of the local adsorbed-phase concentration over the complete pore size distribution range accessible to the adsorbate molecule. The adsorbate-adsorbent interaction energy is related to micropore size via the Lennard-Jones potential theory, and the size exclusion effect is taken into account in the competitive adsorption of different species for a given pore. The MPSD-IAST model predictions are examined with the equilibrium data of mixed gases measured on two commercial activated carbons (Ajax and Norit). The results are compared with those obtained using a MPSD-EL model where the local adsorption isotherm is described by an extended Langmuir equation.

Introduction The adsorption energetic heterogeneity plays an important role in adsorption equilibria as well as kinetics on such an adsorbent as activated carbon. To address this issue, a number of studies in the literature assume that the energetic heterogeneity follows some kind of distribution function, such as the uniform or binomial distribution. With this assumption, the matching energies between different species in the heterogeneous adsorbed phase can be decided by the cumulative energy matching scheme.1-4 However, in addition to the fact that these distribution functions are oversimplified assumptions for real systems, the cumulative energy matching scheme also suffers from the drawback that it does not bring out the physical realities of competition between different adsorbates in the microporous network of adsorbent. It fails to consider two fundamental issues: (1) the energy matching of different species should be within the same pore and (2) the size exclusion effect. To overcome these drawbacks and to address the surface heterogeneity in a more realistic way, some researchers proposed that the micropore size distribution be treated as the intrinsic source of the adsorption energetic heterogeneity. For a physical adsorption process, the adsorbate-pore interaction is then described by the Lennard-Jones potential theory.5,6 This method is later extended to study multicomponent adsorption equilibria7-10 and termed as the MPSD-EL model. In this approach, an extended Langmuir equation * To whom correspondence should be addressed. Email: [email protected]. Tel: (852) 2358 7134. Fax: (852) 2358 0054. (1) Moon, H.; Tien, C. Adsorption of Gas Mixture on Adsorbents with Heterogeneous Surface. Chem. Eng. Sci. 1988, 43, 2967-2980. (2) Valenzuela, D. P.; Myers, A. L.; Talu, O.; Zwiebel, I. Adsorption of Gas Mixtures: Effect of Energetic Heterogeneity. AIChE J. 1988, 34, 397-402. (3) Kapoor, A.; Ritter, J. A.; Yang, R. T. An Extended Langmuir Model for Adsorption of Gas Mixtures on Heterogeneous Surfaces. Langmuir 1990, 6, 660-664. (4) Hu, X.; Do, D. D. Comparing Various Multicomponent Adsorption Equilibrium Models. AIChE J. 1995, 41, 1585-1592. (5) Everett, D. H.; Powl, J. C. Adsorption in Slit-like and Cylindrical Micropores in the Henry’s Law Region. J. Chem. Soc., Faraday Trans. 1 1976, 72, 619-636.

is used to describe the local multicomponent adsorption equilibrium within a given pore and the matching energies between different adsorbates are related to the interaction strength of each adsorbate in the local micropore. The pore size exclusion phenomenon is also implemented in the model. In the MPSD-EL model, the local isotherm has the advantages of being explicit in form and presenting good simplicity in simulation. However, it also requires that the saturation capacities of different adsorbates should be the same to satisfy the thermodynamic consistency. It has been demonstrated that the combination of an extended Langmuir equation and uniform energy distribution can predict multicomponent adsorption equilibria reasonably well only if the saturation capacities of different species are the same11,12 or close to each other.3,8,10,13 However, forcing the saturation capacities of different species to be the same may seriously discount the fitting goodness for the pure component equilibrium data and hence may result in poor prediction for multicomponent (6) Jagiello, J.; Schwarz, J. A. Energetic and Structural Heterogeneity of Activated Carbons Determined Using Dubinin Isotherms and an Adsorption Potential in Model Micropores. J. Colloid Interface Sci. 1992, 154, 225-237. (7) Hu, X.; Do. D. D. Effect of Pore Size Distribution on the Prediction of Multicomponent Adsorption Equilibria. In Fundamentals of Adsorption; LeVan, M. D., ed.; Kluwer Academic Publishers: Boston, MA, 1996; pp 385-392. (8) Wang, K.; Do, D. D. Characterizing the Micropore Size Distribution of Activated Carbon Using Equilibrium Data of Many Adsorbates at Various Temperatures. Langmuir 1997, 13, 6226-6233. (9) Hu, X. Multicomponent Adsorption Equilibrium of Gases in Zeolite: Effect of Pore Size Distribution. Chem. Eng. Commun. 1999, 174, 201-214. (10) Qiao, S. Z.; Wang, K.; Hu, X. Binary Adsorption Equilibrium of Hydrocarbons in Activated Carbon: Effect of Pore Size Distribution. Ind. Eng. Chem. Res., in press. (11) Hu, X.; Do, D. D. Effect of Surface Energetic Heterogeneity on the Kinetics of Adsorption of Gases in Microporous Activated Carbon. Langmuir 1993, 9, 2530-2536. (12) Hu, X.; Do, D. D. Role of Energy Distribution in Multicomponent Sorption Kinetics in Bidispersed Solids. AIChE J. 1993, 39, 16281640. (13) Ahmadpour, A.; Wang, K.; Do, D. D. Comparison of Models on the Prediction of Binary Equilibrium Data of Activated Carbons. AIChE J. 1998, 44, 740-752.

10.1021/la990785q CCC: $19.00 © 2000 American Chemical Society Published on Web 11/12/1999

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equilibria. This phenomenon becomes even more significant when the difference between the saturation capacities of various species is large.4 For such systems the ideal adsorbed solution theory (IAST) offers a good solution. The IAST has the advantage that the prediction for multicomponent equilibria is independent of the choice of isotherm equation provided that the isotherm equation can well fit the pure component equilibrium data.14-16 Therefore, the IAST can be used as the local isotherm to describe the equilibria on each adsorption site for a heterogeneous adsorbent. The overall adsorption equilibrium in this case is represented as the integral of local equilibria over the complete energy distribution range. This model is termed as the HIAST model.2,4,14 In the past, HIAST mainly employs the uniform or binomial energy distribution to account for surface heterogeneity and uses the cumulative energy matching scheme to decide the matching energies between different species. In this paper, the IAST is used to represent the local multicomponent adsorption isotherm within a single pore and the overall adsorption equilibrium is the integral of the local isotherm over the accessible micropore size distribution. This model is called MPSD-IAST. It will be examined with the binary adsorption equilibrium data of gases on two commercial activated carbons (Ajax and Norit). Theory If the micropore size distribution (MPSD) of an activated carbon is represented by the function F(rp), where rp is the pore half-width, the observed adsorption isotherm on the adsorbent can be expressed as the integral of the local isotherm, Cµ(k,rp), over the pore size range accessible to the adsorbate, i.e.

Cµ(k) )

∫r∞ (k)Cµ(k, rp) F(rp) drp min

(1)

where rmin is the minimum half-width of the pore accessible to adsorbate k. For simplicity, the micropore size distribution is assumed to follow a gamma distribution, i.e.

F(rp) )

qν+1rνpe-qrp Γ(ν + 1)

(2)

where q, ν are the two parameters. The local isotherm in eq 1 is represented by the IAST, with the pure component following the Langmuir equation

C0µ(rp)

) Cµs

b0eE(rp)/RTCp 1 + b0eE(rp)/RTCp

(3)

where Cµs is the adsorption saturation capacity, Cp is the gas-phase concentration, R is the gas constant, T is temperature, and b0 is the adsorption affinity at zero energy level. In the iterative calculation of local equilibria with IAST, the size exclusion effect is taken into account. For a species j with a molecular size larger than the lower integration limit, rmin(k) of eq 1, it cannot be adsorbed for those micorpores between rmin(k) and rmin(j). (14) Myers, A. L. Molecular Thermodynamics of Adsorption of Gas and Liquid Mixtures. In Fundamentals of Adsorption; Liapis, A. I., Ed.; Engineering Foundation: New York, 1987. (15) Richer, E.; Schuttz, W.; Myers, A. L. Effect of Adsorption Equation on Prediction of Multicomponent Adsorption Equilibria by the Ideal Adsorption Solution Theory. Chem. Eng. Sci. 1989, 44, 1609-1616. (16) Hu, X.; Do, D. D. Multicomponent Adsorption Kinetics of Hydrocarbons onto Activated Carbon: Effect of Adsorption Equilibrium Equations. Chem. Eng. Sci. 1992, 47, 1715-1725.

Since the adsorption energetic heterogeneity is assumed to be induced by the structural heterogeneity, i.e., the size distribution of the slit-shaped micropore for activated carbon, the adsorbate-pore interaction energy, E(rp) in eq 3, can be related to the adsorption potential minimum in the local micropore. In this study, the micropore takes the configuration of that described by the Lennard-Jones 10-4 potential,5 which is expressed as

{( ) ( )

5 2 r0(k) up(k,z) ) u/s (k) 3 5 z

10

r0(k) 4 + z 10 r0(k) 2 r0(k) 5 2rp - z 2rp - z -

(

) (

)} 4

(4)

where z is the center-center distance between an adsorbate molecule and one side of the graphite lattice plane (pore wall), and r0 is the collision diameter between an adsorbate molecule (rg0) and a carbon molecule,5 i.e.

1 r0 ) (rg0 + 3.40 Å) 2

(5)

The parameter u/s is the depth of the Lennard-Jones potential minimum for a single lattice plane. The adsorbate-adsorbent interaction energy is taken as the negative of the potential energy minimum inside the pore.6,17 Experimental Section For Ajax-activated carbon, both the pure component and the multicomponent adsorption equilibria were measured on volumetric rigs.11,13 The binary adsorption experiments were performed at a constant pressure of 66.7 kPa. The adsorption equilibria of three binary gas mixtures, CH4-C2H6, CH4-C3H8, and CH4-CO2, were measured on the adsorbent. For Noritactivated carbon, the pure component adsorption isotherms of methane, ethane, and propane were measured with a volumetric rig while the multicomponent adsorption equilibria of the binary gas mixtures among these three adsorbates were measured on a differential adsorber bed (DAB) rig. The bulk-phase pressure for multicomponent experiments was kept at a constant pressure of 50 kPa. The detailed experimental procedures for measuring adsorption equilibria with volumetric and DAB rigs can be found in ref 10.

Results and Discussion Micropore Size Distribution of the Activated Carbons. The MPSDs for the two carbon samples were obtained in our previous studies with the MPSD-EL model. The parameters for the gamma distribution function are q ) 21.01 Å-1, ν ) 98.14 for Norit carbon10 and q ) 21.57 Å-1, ν ) 97.87 for Ajax carbon.8 Figure 1 shows graphically the MPSDs of the two carbons (lines). Also shown in the figure are the minimal accessible pore half-widths, rmin, of methane, ethane, propane, and CO2 molecules, respectively. Here rmin is defined as the halfwidth of pores in which the adsorption potential is zero (rmin ) 0.8583r0 for 10-4 potential). The molecule size of each adsorbate was taken from Breck.18 We see that the Norit carbon has a slightly larger mean pore size than the Ajax carbon, and only a little portion of pores in the two adsorbents is excluded for these adsorbate molecules. Single-Component Adsorption. First, the pure component equilibrium data on Norit carbon are used to (17) Hu, X.; Do, D. D. Effect of Surface Heterogeneity on the Adsorption Kinetics of Gases in Activated Carbon: Pore Size Distribution vs Energy Distribution. Langmuir 1994, 10, 3296-3302. (18) Breck, D. W. Zeolite Molecular Sieves: Structure, Chemistry and Use; John Wiley & Sons: New York, 1974.

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Figure 1. Micropore size distribution of Ajax- and Noritactivated carbons. Table 1. Isotherm Parameters of Methane, Ethane, and Propane on Norit-Activated Carbon species

303 K

methane ethane propane

6.1521 7.0157 4.6181

Cµs (mmol/g) 333 K 363 K 5.1647 6.2929 4.1139

4.1453 5.5191 3.6213

u/s (kJ/mol)

b0 × 104 (kPa-1)

8.1980 14.962 12.809

0.4133 0.1100 1.5282

optimize the isotherm parameters (Cµs, u/s , b0) with the related MPSD in Figure 1. The isotherm parameters of an adsorbate were obtained by fitting its related experimental data at three temperatures, 303, 333, and 363 K, simultaneously to the model. The derived isotherm parameters for methane, ethane, and propane are tabulated in Table 1. During optimization, Cµs is both temperature and species dependent while the other two parameters, b0 and u/s , are temperature independent but species dependent. Figure 2 shows the model fittings (solid lines) and the pure component equilibrium data (symbols) of the three species on Norit-activated carbon. It is seen in Figure 2 that the model with variable Cµs for different species can well fit the equilibrium data of the three species over the experimental temperature range. In the MPSD-EL model, since an extended Langmuir isotherm is used to describe the local multicomponent adsorption equilibrium, the maximum adsorption capacity is usually forced to be the same for all components to satisfy the thermodynamic consistence.7,9 To study how this restriction affects the single-component data fitting and multicomponent prediction, another methodology is carried out to reoptimize the pure component equilibrium parameters for each species with the above constraint, all species having the same maximum adsorption capacity, enforced. The new parameters, listed in Table 2, are obtained by fitting the experimental data of three species at three different temperatures (a total of nine isotherms) simultaneously. The model fittings with this constraint for each species are shown in Figure 2 as dashed lines. It can be seen that the fitting is not as good as the model without this restriction (solid lines). The pure component isotherm parameters for methane, ethane, propane, and CO2 on Ajax-activated carbon are also derived using the two optimization schemes mentioned above, respectively, which are shown in Tables 3 and 4. The isotherm parameters in Table 4 are obtained by fitting the experimental data of three adsorbates, methane, ethane, and propane, at two temperatures, 283 and 303 K, simultaneously. Figure 3 shows the model

Figure 2. Adsorption isotherm data and model fittings of methane, ethane, and propane on Norit-activated carbon: (s) different Cµs; (-‚-) same Cµs. Table 2. Isotherm Parameters of Methane, Ethane, and Propane on Norit-Activated Carbon (Same Cµs for Different Species) species

303 K

methane ethane propane

4.7272

Cµs (mmol/g) 333 K 363 K 4.0703

3.4598

u/s (kJ/mol)

b0 × 104 (kPa-1)

9.0296 11.355 12.251

0.3877 1.7067 2.0176

Table 3. Isotherm Parameters of Methane, Ethane, Propane, and CO2 on Ajax-Activated Carbon Cµs (mmol/g) species

258 K

273 K

u/s b0 × 104 283 K 303 K 333 K (kJ/mol) (kPa-1)

methane 6.9549 5.4714 5.1908 4.1423 7.5200 ethane 9.6351 8.9840 8.2742 12.719 propane 7.1353 7.0243 6.8372 18.584 CO2 13.807 11.266 8.5100 9.1824

0.7228 0.1395 0.01488 0.8396

fittings (lines) and the pure component adsorption equilibrium data (symbols) of the four species on the Ajax carbon. Again the MPSD model with variable Cµs fits the pure component isotherm data better than the model using the same Cµs. Binary Adsorption Equilibria. In this section, three equilibrium models will be employed to predict the binary adsorption equilibrium data measured on two commercial activated carbons by using the related equilibrium information of the pure component system only. They are

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Table 4. Isotherm Parameter of Methane, Ethane, Propane, and CO2 on Ajax-Activated Carbon (Same Cµs for Different Species) species methane ethane propane

Cµs (mmol/g) 283 K 303 K 8.3540

8.0803

u/s (kJ/mol)

b0 × 104 (kPa-1)

10.678 11.887 21.725

0.04645 0.3128 0.1151

Figure 3. Adsorption isotherm data and model fittings of methane, ethane, propane, and carbon dioxide on Ajax-activated carbon: (s) different Cµs; (- - -) same Cµs.

Figure 4. Binary adsorption equilibria of ethane-propane on Norit-activated carbon at 50 kPa: (s) MPSD-IAST; (- - -) MPSD-EL (different Cµs); (-‚-) MPSD-EL (same Cµs).

the following: (1) the MPSD-IAST model, (2) the MPSDEL model assuming different Cµs for various species, and (3) the MPSD-EL model assuming the same Cµs for all species. Models 1 and 2 have the same single-component isotherm parameters, which are listed in Table 1 for Norit carbon and Table 3 for Ajax carbon, respectively. For model 3 the pure component equilibrium data are listed in Tables 2 and 4 for Norit and Ajax carbons, respectively. The three models are first employed to simulate the binary equilibrium data of hydrocarbon gases on Noritactivated carbon. Figure 4a shows the experimental equilibrium data (symbols) of ethane-propane on Norit carbon at 303 K. Also shown in the same figure are the prediction results from each model. It is seen that the MPSD-IAST model (solid lines) can reasonably simulate the experimental data for both ethane and propane. The MPSD-EL model with different Cµs (dashed lines) gives a good prediction for propane but a bad prediction for ethane. The reason for this deviation is possibly that the saturation capacity of ethane (7.0157 mmol/g) significantly differs from that of propane (4.6181 mmol/g), a 52% difference based on the smaller value (propane). Hence the use of extended Langmuir equation as the local adsorption equilibria can result in some error. However, with special treatment in the pure component equilibrium data analysis, i.e., forcing the saturation capacities of different species to be the same, the thermodynamic consistency is satisfied and the MPSD-EL model’s prediction for the light species is improved, as can be seen as the dashed-dotted lines in Figure 4. But this improvement also depends on the fact that the model’s capability in fitting the pure component isotherm data is not seriously

discounted. This point will be further investigated later in this paper. Parts b and c of Figure 4 show the model predictions (lines) and the experimental data (symbols) for the same ethane-propane system at two other temperatures: 333 and 363 K. It is seen that the MPSD-IAST model (solid lines) again gives good prediction for both ethane and propane at the two temperatures, which justifies the temperature dependence of the MPSD-IAST model. The MPSD-EL model with different Cµs still gives an inferior prediction for ethane. The simulation results from the MPSD-EL model with same Cµs (dashed-dotted lines) also present some deviation in the prediction of the binary ethane-propane adsorption data on Norit carbon at 363 K. This difference between the predictions of the MPSDEL model with same Cµs and the experimental data seems to originate from the deviation in fitting the pure component adsorption data, as can be seen in Figure 2 where there is some obvious deviation between the model fitting (dashed lines) and the pure component equilibrium data of the two species at this temperature. This is in line with the conclusion drawn by Hu and Do4 that a small error in fitting pure component equilibrium data can cause a large error in the prediction of multicomponent equilibria. Then we turn to the binary adsorption equilibria of the methane-ethane system on Norit carbon. Parts a and b of Figure 5 show the model predictions (lines) and the experimental data (symbols) of the methane-ethane system at 303 and 333 K, respectively. We see that the difference between the simulation results from the MPSD-EL model with different Cµs (dashed lines) and

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Figure 5. Binary adsorption equilibria of methane-ethane on Norit-activated carbon at 50 kPa: (s) MPSD-IAST; (- - -) MPSD-EL (different Cµs); (-‚-) MPSD-EL (same Cµs).

the MPSD-IAST model (solid lines) is narrowed compared with that of the ethane-propane system shown in Figure 4. This is expected owing to the fact that the saturation capacities of methane (6.1521 mmol/g at 303 K) and ethane (7.0157 mmol/g at 303 K) are closer to each other (14% difference) than those of ethane and propane (52% difference). The similar phenomenon can also be observed when comparing the prediction results from the three models for the binary adsorption equilibria of methane-propane on Norit carbon at three different temperatures, 303, 333, and 363 K. Figure 6a-c shows the experimental data (symbols) and prediction results (lines). We see once again that the MPSD-IAST predicts the data very well. The MPSD-EL model with variable Cµs almost superimposes with the MPSD-IAST because the saturation capacities of the two adsorbates are close to each other and the adsorption affinities of methane and propane are significantly different (Figure 2) so that propane adsorption behaves like a single-component system. The prediction deviation for propane by the MPSD-EL model with the same Cµs is due to the error in fitting the pure propane isotherm data (Figure 2), resulting from the constraint on the saturation capacities of different species. To further examine the predictive capability of the three models, the adsorption equilibria of binary gas mixtures measured on Ajax-activated carbon are employed in the study. The binary systems investigated here are methaneethane, methane-propane, and methane-carbon dioxide systems. Parts a and b of Figure 7 show the binary adsorption isotherms of methane-ethane and methanepropane systems on Ajax carbon at 303 K (symbols), respectively. The prediction results from the three models are also illustrated in these two figures as lines. It is seen that the MPSD-IAST model (solid lines) predicts the data reasonably well for each binary system. The MPSD-EL

Figure 6. Binary adsorption equilibria of methane-propane on Norit-activated carbon at 50 kPa: (s) MPSD-IAST; (- - -) MPSD-EL (different Cµs); (-‚-) MPSD-EL (same Cµs).

model with different Cµs (dashed lines) also predicts well for both systems. The MPSD-EL model with the same Cµs (dashed-dotted lines), however, presents some error for ethane. As in the case of Norit-activated carbon, this prediction error is caused by the discrepancy between the pure component experimental data and the model’s fitting for pure component equilibrium data. It can be seen in Figure 3 that the fittings, which constrain the Cµs to be the same for different species (dashed line), give some deviation to the experimental data. So we further confirm that, by forcing the maximum adsorption capacity to be the same for all species, the MPSD-EL model with the same Cµs may give good prediction result only when the fittings for pure component isotherm are good enough. Otherwise the prediction in this case will be inferior to the same MPSD-EL model, but allowing the Cµs in the Langmuir equation to be species dependent. Finally, the MPSD-IAST model and the MPSD-EL model with different Cµs are employed to predict the binary adsorption equilibria of methane-CO2 system on Ajaxactivated carbon. The MPSD-EL model with the same Cµs is not examined here because the adsorption isotherm is not measured for all species at 273 K; this is another disadvantage for this model. Figure 8a shows the model predictions (lines) and the experimental data (symbols) for such a system at 303 K. It is seen that the MPSDIAST model (solid lines) predicts much better than the MPSD-EL model with different Cµs (dashed lines) at this temperature. The reason is that the maximum adsorption capacity of methane (4.1423 mmol/g) is significantly different from that of CO2 (8.510 mmol/g), representing a difference of 105%. Hence the MPSD-EL model with

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Figure 7. Binary adsorption equilibria on Ajax-activated carbon at 303 K, 66.7 kPa: (a) methane-ethane; (b) methanepropane. (s) MPSD-IAST; (- - -) MPSD-EL (different Cµs); (-‚-) MPSD-EL (same Cµs).

different Cµs produces an inferior prediction result, possibly owing to the inability to meet the thermodynamic consistency. To further investigate the effect of temperature on adsorption equilibria for the two models, the binary data of the methane-CO2 system on Ajax-activated carbon at 273 K are simulated with the two models. The corresponding prediction results (lines) and the experimental data (symbols) are presented in Figure 8b. Both models predict the data reasonably well, but the MPSD-IAST model predicts slightly better than the MPSD-EL model. The temperature dependence of both models is seen to be reliable. To compare the predictive capabilities of the three models quantitatively, the average relative error (ARE) between the model predictions and the equilibrium data on Ajax carbon are calculated and listed in Table 5 for each species in different binary systems. The ARE is defined as follows:3

ARE )

100 N

N

(

∑ abs

k)1

)

Cµ,cal - Cµ,exp Cµ,exp

(6)

where N is the number of data points and Cµ,cal and Cµ,exp are the simulated adsorption equilibrium concentration of a species and its corresponding experimental value, respectively. We can see from the values of the ARE in Table 5 that the MPSD-IAST model gives better prediction results for most of the binary systems, except that for methane in the methane-CO2 system at 273 K. The MPSD-EL

Figure 8. Binary adsorption equilibria of methane-CO2 at 66.7 kPa: (s) MPSD-IAST; (- - -) MPSD-EL (different Cµs). Table 5. Relative Average Error of Binary Adsorption on Ajax-Activated Carbon 303 K ARE (%)

C1

C2

303 K C1

C3

303 K C1

CO2

273 K C1

CO2

MPSD-IAST 15.06 9.10 18.30 6.94 12.57 14.99 25.54 14.97 MPSD-EL 32.56 8.42 22.73 12.34 13.78 21.51 10.34 21.78 (different Cµs) MPSD-EL 15.85 11.70 20.81 9.23 (same Cµs)

model with the same Cµs gives slightly better predictions than the MPSD-EL model with different Cµs for binary adsorption equilibria of methane-ethane and methanepropane systems on Ajax-activated carbon at 303 K. These quantitative results are consistent with our previous analysis on the performance of each model for the binary adsorption equilibria on Norit-activated carbon. Conclusions A new multicomponent adsorption isotherm model is proposed using a micropore size distribution to represent the energetic heterogeneity of the adsorbent and the ideal adsorbed solution theory to describe the local multicomponent adsorption equilibrium. The size exclusion effect is taken into account in the competition of different species for a given pore. The MPSD-IAST model can fit the singlecomponent adsorption isotherm well and is thermodynamically consistent in the prediction of multicomponent adsorption equilibrium. It overcomes the drawbacks in the MPSD-EL model that either the single-component isotherm data fitting is not good enough if the saturation adsorption capacity is forced to be the same for all species

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or it violates the thermodynamics otherwise. The MPSDIAST model is validated with experimental equilibrium data on two activated carbons (Ajax and Norit) over a range of temperature and adsorbate combinations. It is found that, using the pure component equilibrium information, the MPSD-IAST model is able to predict binary equilibria reliably well under the experimental conditions. Glossary ARE b0 Cp Cµ C0µ Cµs E EL IAST MPSD q R

average relative error affinity constant at zero energy level (kPa-1) adsorbate concentration (kPa) adsorbed concentration in the particle (mol/g) adsorbed-phase concentration, evaluated by pure component isotherm (mol/g) adsorption saturation capacity (mol/g) adsorbate-adsorbent interaction energy (kJ/mol) extended Langmuir ideal adsorbed solution theory micropore size distribution gamma distribution parameter (Å-1) gas constant [kJ/(mol K)]

Qiao et al. rmin r0 rp T up u/p u/s Y z

minimum accessible pore half-width (Å) Lennard-Jones collision diameter micropore half-width (Å) temperature (K) gas-solid potential in slitlike parallel walls (kJ/ mol) depth of the potential minimum depth of the potential minimum on single lattice layer (kJ/mol) mole fraction in the gas phase distance between the molecule and the pore wall (Å)

Greek Symbols Γ ν

gamma function gamma distribution parameter

Acknowledgment. This work was supported by the Croucher Foundation and the Research Grants Council of Hong Kong. LA990785Q