Adsorption Equilibria of Binary Gas Mixtures on Graphitized Carbon

Dec 22, 2011 - real adsorption solution theory (RAST) has been used to analyze the property of the adsorbed mixtures. The activity coefficients have b...
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Adsorption Equilibria of Binary Gas Mixtures on Graphitized Carbon Black Ming Li,* Erling Xu, Tingliang Wang, and Juan Liu Department of Chemistry, Shanghai Tongji University, Shanghai, P. R. China ABSTRACT: Adsorption equilibria for binary gas mixtures (methane−carbon dioxide, methane−ethane, and carbon dioxide−ethane) on the graphitized carbon black STH-2 were measured by the open flow method at 293.2 K. The experimental pressure range was (0 to 1.6) MPa. The extended Langmuir (EL) model and the ideal adsorption solution theory (IAST) have been adopted to predict the equilibria of binary gas mixtures. The results indicate that gas mixtures adsorbed on the homogeneous surface of STH-2 exhibit the nonideal behavior, which is mainly induced by adsorbate−adsorbate interactions. The real adsorption solution theory (RAST) has been used to analyze the property of the adsorbed mixtures. The activity coefficients have been correlated with the Wilson equation. The investigation demonstrates that the nonideality of adsorbed phase is completely dissimilar with the bulk liquid phase. The adsorption of the heavier component would benefit the adsorption of the lighter component. or the ideal adsorption solution theory (MPSD-IAST).5−7 Those methods have been proven with more acceptable predictions for most adsorption systems. The interaction between different kinds of adsorbate is also an important contribution to nonidealities of the adsorbed phase. This has not been investigated extensively so far. The multispace adsorption model (MSAM), proposed by Gusev et al., has taken into account the inherent nonuniformity of the adsorbate.8 Ritter et al. considered the effects of differences in the molecular size of the components in a gas mixture.9 The covolume-dependent (CVD) mixing rule has been suggested as a binding bridge between the molecular size and the molecular interaction to achieve more accurate prediction for multicomponent gas adsorption systems.10 The work of Vaart et al. has shown that the properties of the CH4−CO2 phase adsorbed on activated carbon are completely different from the bulk solution.11 It is concluded that new prediction models should be developed encompassing both nonideal solution behavior and surface heterogeneity. Accurate calculation of mixed gas adsorption data from single component adsorption isotherms requires nonideality in the adsorbed phase to be taken into account. If interactions between adsorbate molecules were not considered, the discrepancy between experimental data and theoretical prediction would be higher.12 As a consequence, more experimental processes and more theoretical analysis are needed to improve the understanding of adsorbate lateral interactions. In this work, adsorption equilibria for various binary gas mixtures on the graphitized carbon black (GCB) are presented. Because the graphitized carbon black could be considered with

1. INTRODUCTION Adsorption equilibrium data of mixed gases on solid materials are crucial to the design and operation of gas adsorption separation process.1 With wide industrial applications of gas adsorption separation, the development of theoretical models for multicomponent adsorption equilibria is a worthwhile goal. Since experimentation to obtain adsorption equilibrium data of a gas mixture is a tedious and time-consuming process, it is an acceptable approach to use adsorption isotherms of pure components to predict multicomponent adsorption equilibrium data.2 A number of models have been put forward and investigated to achieve adsorption equilibria of gas mixtures, including the extended Langmuir (EL) model, the ideal adsorption solution theory (IAST), the real adsorption solution theory (RAST), the Flory−Huggins vacancy solution model (FHVSM), and so on. The IAST, proposed by Myers and Prausnitz, is a thermodynamically rigorous theory on the basis of the ideal mixing rule of individual adsorbed components at constant spreading pressure.3 It provides a convenient approach to calculate adsorption data of mixtures from pure gas isotherms. If experimental data demonstrate some deviations from IAST, it is usually attributed to the nonideality of the adsorbed phase. The RAST uses activity coefficients to describe the nonidealty of the adsorbed phase, which have to be calculated from binary gas adsorption equilibrium data.4 There are two main sources for contributions to the nonideality of adsorbed phase. One is the adsorbent with energetically heterogeneous surface, the other is adsorbate− adsorbate interactions. Many efforts have been made to consider the effect of heterogeneous potential on the adsorption behavior, including the heterogeneous ideal adsorbed solution theory (HIAST), models with micropore size distribution and the extended Langmuir equation (MPSD-EL) © 2011 American Chemical Society

Received: August 29, 2011 Revised: December 17, 2011 Published: December 22, 2011 2582

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a homogeneous surface, the nonideality of adsorbed phase should be mainly attributed to the adsorbed phase nonuniformity. The investigation attempts to explore the properties of the mixed adsorbed phase.

Table 1. Adsorption Equilibrium Data of Pure Methane, Carbon Dioxide, and Ethane on GCB STH-2 at 293.2 K CH4

2. EXPERIMENTAL SECTION 2.1. Materials. The adsorbent used in experiments was the graphitized carbon black STH-2 supplied by Lanzhou Atech Technologies Company. It was in granular form with particle sizes of 0.85−1.20 mm. The specific surface area of GCB STH-2 was 65.13 m2.g−1 calculated by nitrogen adsorption data at 77 K, which was measured using a Tristar 3000 static volumetric adsorption analyzer from Micromeritics. The purities of methane, carbon dioxide, ethane, and helium were all higher than 99.99%. The gas mixtures were made by pure components charging into a cylinder which had been under vacuum for at least 24 h. The composition of mixtures was analyzed by the TCD detector of a gas chromatography (Techcomp 7890II, China). 2.2. Single Gas Adsorption Experiments. Adsorption equilibrium isotherms of pure methane, carbon dioxide, and ethane at 293.2 K, shown in Figure 1, were measured by the volumetric method. The

CO2

C2H6

p/MPa

n/mol·kg−1

p/MPa

n/mol·kg−1

p/MPa

n/mol·kg−1

0.0425 0.1101 0.1775 0.2452 0.3350 0.4275 0.6100 0.8550 1.2150 1.6475

0.0074 0.0241 0.0409 0.0546 0.0678 0.0816 0.1128 0.1451 0.1939 0.2414

0.0375 0.0950 0.1675 0.2350 0.3050 0.3725 0.4500 0.5250 0.7650 1.4800

0.0084 0.0261 0.0523 0.0774 0.1082 0.1386 0.1721 0.1959 0.2781 0.4767

0.0250 0.0675 0.1200 0.1800 0.2475 0.3225 0.4000 0.4775 0.5575 0.6600 0.8425 1.2000

0.0412 0.1098 0.1680 0.2246 0.2747 0.3041 0.3300 0.3516 0.3745 0.3950 0.4373 0.5166

stechnik PAA 200, Switzerland) with the range 0−5 MPa (±0.00125 MPa). The gas tank was designed to collect the desorbed gas. Its volume is 778.93 mL (±0.05 mL) through water titration. Two thermostats, thermostat 1 and thermostat 2, were used to keep the temperatures of the adsorption column and the gas tank at constant values, respectively. The fluctuation of temperature was controlled within ±0.1 K. After evacuation of the adsorption system for 8 h, helium flowed into the adsorption column to enable the value of the adsorption pressure. Then, the mixed gas flowed with a certain flow rate into the adsorption column. The outlet gas concentration was analyzed by the gas chromatography until it was same with the inlet value for at least 1 h, which means the adsorption approaching the equilibrium. Once adsorption equilibrium was obtained, the adsorption column was isolated. The adsorption column was heated to 368 K to degas the adsorbate. At same time, helium with slow flow rate was charged into the adsorption column to purge the adsorbate into the gas tank. Because of no micropore in the STH-2, the desorption process was eventually completed within 4 h. Thus, the mixed gas in the gas tank was isolated until all its properties were in a stable state. Adsorption equilibrium data for the gas mixture could be determined on the basis of the mass balance. The dead space of the adsorption column was determined using the helium measurements at 293.2 K. The amount adsorbed ni,ad of component i is calculated by

Figure 1. Adsorption equilibrium data of CH4, CO2, and C2H6 on STH-2 GCB at 293.2 K. range of equilibrium pressure is 0−1.6 MPa. The mass of GCB STH-2 used is 19.540 ± 0.001 g. Helium was adopted to determine the dead space since it could be regarded as with no adsorption under experimental conditions. The experimental data are listed in Table 1. Details of the experimental apparatus and experimental procedures have been illustrated in the previous work.13 2.3. Binary Gas Adsorption Experiments. Adsorption equilibrium data of binary gas mixtures, including CH4 (1) − CO2 (2), CH4 (1) − C2H6 (2), and CO2 (1) − C2H6 (2), were measured by the open flow system. Component 1 is the lighter component having relatively weak molecular interactions and component 2 is the heavier component having relatively strong molecular interactions. The experimental temperature is 293.2 K and the equilibrium pressure range is 0−1.6 MPa. The apparatus for the mixture adsorption measurement is schematically illustrated in Figure 2, which is capable of measuring amounts adsorbed at different pressures with a constant gas phase composition. The adsorption column, with 150 mm length and 32 mm internal diameter, was filled with the GCB STH-2 (29.520 ± 0.001 g). Two mass flow controllers (MFC1 and MFC2 supplied by Beijing Sevenstar Electronics, China) were involved to control the flow rates of the gas stream into the adsorption column. The accuracy of MFC is 0.3% over the scale range. A back-pressure regulator was used to maintain the adsorption pressure at the desired level. The values of pressure were measured through two transducers (Keller Druckmes-

ni,ad = (ni,GT − ni,AC)/m

(1)

where ni,GT and ni,AC are the amounts of component i in the gas tank and in the dead space of the adsorption column, respectively, and m is the mass of the adsorbent. The Benedict-Webb-Rubin-Starling (BWRS) equation was chosen as the gas equation of state to carry out the above calculation on the basis of the determined pressure, the temperature, and the volume. Adsorption equilibrium data for binary mixtures are listed in Tables 2−4. To check the reliability of experimental data, the open flow method was also used to measure pure methane adsorption equilibrium data, which may have the largest experimental uncertainty. A comparison of experimental data between the static volumetric method and the open flow method is shown in Figure 3. It can be seen that the results are satisfactory.

3. RESULTS AND DISCUSSION 3.1. Extended Langmuir Model (EL). The extended Langmuir equation is the simplest model for prediction of multicomponent adsorption equilibria. To use the extended Langmuir equation, experimental adsorption data for pure component should be first expressed by the Langmuir 2583

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Figure 2. Schematic of the experimental setup using the open flow method. (PR, pressure regulator; MFC1 and MFC2, mass flow controllers; AC, adsorption column; PT, pressure transducer; GS, gas sample; T1 and T2, thermostat; GT, gas tank; BPR, back-pressure regulator; VP, vacuum pump.).

Table 2. Adsorption Equilibrium Data of the CH4 (1)−CO2 (2) Mixture on GCB STH-2 at 293.2 K

Table 3. Adsorption Equilibrium Data of the CH4 (1)−C2H6 (2) Mixture on GCB STH-2 at 293.2 K

amount adsorbed/mol·kg−1 p/MPa 0.2306 0.4125 0.6138 0.8244 1.0044 1.2056 0.2094 0.4169 0.6131 0.8138 1.0150 1.1988

n1

n2

y1 = 65.98%/y2 = 34.02% 0.0328 0.0308 0.0533 0.0519 0.0765 0.0785 0.1048 0.1061 0.1174 0.1223 0.1223 0.1344 y1 = 84.44%/y2 = 15.56% 0.0412 0.0119 0.0717 0.0225 0.1034 0.0335 0.1317 0.0438 0.1598 0.0515 0.1834 0.0625

amount adsorbed/mol·kg−1 nt

p/MPa

0.0636 0.1052 0.1550 0.2109 0.2397 0.2567

0.2094 0.4081 0.6094 0.7919 0.9875 1.2088 1.4100 1.6281

0.0531 0.0943 0.1369 0.1755 0.2113 0.2459

0.2038 0.4075 0.6119 0.8150 1.0256 1.1994 1.3988 1.6219

equation bp n = 1 + bp n0

(2) 2584

n1

n2

y1 = 80.31%/y2 = 19.69% 0.0326 0.0536 0.0607 0.1003 0.0789 0.1305 0.0973 0.1536 0.1131 0.1716 0.1268 0.1926 0.1391 0.2034 0.1533 0.2097 y1 = 56.29%/y2 = 43.71% 0.0207 0.1195 0.0327 0.1917 0.0433 0.2335 0.0541 0.2647 0.0611 0.2914 0.0667 0.3055 0.0715 0.3274 0.0826 0.3562

nt 0.0862 0.1610 0.2094 0.2509 0.2847 0.3194 0.3425 0.3630 0.1401 0.2244 0.2768 0.3188 0.3525 0.3722 0.3989 0.4388

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Table 4. Adsorption Equilibrium Data of the CO2 (1)−C2H6 (2) Mixture on GCB STH-2 at 293.2 K

Table 5. Parameters of the Langmuir Equation in Fitting the Experimental Data of Methane, Carbon Dioxide, and Ethane on GCB STH-2 at 293.2 K

amount adsorbed/mol·kg−1 p/MPa

n1

n2

y1 = 25.42%/y2 = 74.58% 0.0163 0.1839 0.0272 0.2642 0.0330 0.305 0.0407 0.3476 0.0497 0.3902 0.0604 0.4384 0.0661 0.469 0.0758 0.505 y1 = 44.30%/y2 = 55.70% 0.0282 0.1441 0.0484 0.2111 0.0632 0.2572 0.0789 0.2977 0.0919 0.3295 0.1097 0.3655 0.1194 0.3866 0.1295 0.4115

0.2119 0.4181 0.6275 0.8244 1.0362 1.2356 1.4262 1.6144 0.2088 0.4138 0.6100 0.8156 1.0287 1.2163 1.4019 1.6288

nt

b/MPa−1

n0/mol·kg−1

δ

0.3138 0.1978 2.3777

0.7037 2.0730 0.6849

0.9991 0.9955 0.9904

CH4 CO2 C2H6

0.2003 0.2913 0.338 0.3883 0.4399 0.4988 0.5351 0.5808

The extended Langmuir equation is so convenient that it would greatly shorten the computation time of adsorption simulation processes. However, the thermodynamic consistency requires that the saturation adsorption capacity is the same for all components. In this work, the fitness of the Langmuir equation does not meet this condition. It aims to get good description of pure components, which may improve prediction accuracy of multicomponent adsorption equilibria.14 The prediction results are presented in Table 6. It can be observed

0.1723 0.2594 0.3205 0.3766 0.4214 0.4752 0.5060 0.5410

Table 6. Prediction Results of Binary Gas Mixtures on GCB STH-2 CH4 (1)-CO2 (2) Δn1 Δn2 Δx1 Δx2 Δnt

CH4 (1)-C2H6 (2)

CO2 (1)-C2H6 (2)

E-L

IAST

E-L

IAST

E-L

IAST

5.71 5.51 2.44 4.22 5.02

7.22 4.64 2.83 7.07 4.45

7.58 7.95 10.19 4.26 3.90

7.10 8.45 10.12 4.39 4.36

18.85 9.57 22.58 4.49 6.04

10.90 6.17 3.89 0.75 7.22

that, for CH4 (1) − CO2 (2), both the amount adsorbed and the adsorbate compositions could be acceptable, while for the CO2 (1) − C2H6 (2), the prediction deviation of the amount adsorbed for CO2 approaches 19%. 3.2. Ideal Adsorption Solution Theory (IAST). The IAST model assumes that the adsorbed phase of a mixture is thermodynamically ideal. The equilibrium relationships for the adsorption of a mixture can be derived directly from the isotherms of pure components. For a binary mixture consisting of component 1 and component 2, the prediction could be executed from the Gibbs equation and the Raoult’s law: Figure 3. Comparison of methane adsorption isotherms on the GCB STH-2 obtained by the volumetric method and the open flow method.

∫0

where n is the amount adsorbed at equilibrium, n0 is the saturated adsorption capacity, b is the Langmuir constant, and p is the equilibrium pressure. For thermodynamic considerations, the fugacity has replaced the pressure through the BWRS equation in the following discussion. The fitness of the Langmuir equation is determined by the mean relative deviation δ

∑N j = 1 (nj ,cal

δ=

ni0

=

P20

n2 dp p

(5)

(6)

2

∑ xi = 1

2

(7)

i=1

(3)

where π is the spreading pressure, y and x are mole fractions of the gas and the adsorbed species respectively, and P0 is defined as the gas pressure of a pure component at the spreading pressure π. The prediction accuracy are evaluated by

bipi

1 + ∑im= 1 bipi

∫0

Py2 = P20(π)x2

The regression results are listed in Table 5. Thus, all parameters of pure component could be extended to predict multicomponent adsorption equilibria through the extended Langmuir equation

ni

n1 dp = p

Py1 = P10(π)x1

− nj ,exp)

N

P10

Δni = (4) 2585

1 N

N

∑ j=1

nij ,exp − nij × 100% nij ,exp

(8)

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Article

N

∑ j=1

N

∑ j=1

ntj ,exp − ntj ntj ,exp

calculated through eq 11. The Wilson equation is selected to correlate the activity coefficients, which is expressed by

× 100%

xij ,exp − xij × 100% xij ,exp

(9)

ln γ1 = − ln(x1 + Λ12x2) ⎤ ⎡ Λ12 Λ21 + x 2⎢ − ⎥ x2 + Λ21x1 ⎦ ⎣ x1 + Λ12x2

(10)

ln γ2 = − ln(x2 + Λ21x1) ⎤ ⎡ Λ12 Λ21 − x1⎢ − ⎥ x2 + Λ21x1 ⎦ ⎣ x1 + Λ12x2

where nt is the total amount adsorbed. The prediction results are listed in Table 6. It can be shown that the IAST model could not predict the adsorption equilibrium data exactly. Figure 4 presents the amount adsorbed of CH4 predicted by the

(constant π and T )

(12)

where Λ12 and Λ21 are binary interaction parameters. The obtained activity coefficients are plotted as a function of adsorbed phase composition in Figures 5−7 at different

Figure 4. Comparison of experimental data and prediction of the IAST and the EL for CH4 in the CH4 (1)−C2H6 (2) system (y1/y2 = 56.29%/43.71%).

EL equation and the IAST model in the CH4 (1) − C2H6 (2) with the composition (y1 = 56.29% and y2 = 43.71%). Over the low pressure range, both the EL equation and the IAST model could make the acceptable prediction. If the pressure is higher than 1 MPa, the predicted values from the IAST model or the EL equation become lower than the experimental data. This deviation should be attributed to the nonideality of the adsorbed phase, because the adsorbate lateral interactions become stronger with higher surface coverage. 3.3. Real Adsorption Solution Theory (RAST). If the adsorbed phase performs nonideal behavior, the IAST model could be revised to the RAST model with the activity coefficients. The Raoult’s law of eq 6 is now replaced by

Pyi = Pi0(π)xi γi

Figure 5. Experimental and fitted Wilson equation activity coefficients for CH4 (1)−CO2 (2) adsorbate mixtures at 293.2 K. Solid symbols: γ1 for CH4; open symbols: γ2 for CO2. Square: π* = 0.15 mol/kg; circle: π* = 0.20 mol/kg; triangle: π* = 0.25 mol/kg.

reduced spreading pressures π* (π* = πA/RT). The calculated binary interaction parameters, Λ12 and Λ21, are given in Table 7. To analyze the property of the adsorbed phase, the interaction parameters Λ12 and Λ21 of the Wilson equation for the bulk liquid mixtures are also given in Table 7. It can be seen that the interactions between two components in the adsorbed phase are quite different from those in the bulk liquid state. In the bulk liquid phase for CH4 (1) − CO2 (2), the low values of Λ12 and Λ21 indicate that there are no strong interactions between the two species. On the other hand, in the CH4 (1) − CO2 (2) adsorbed phase, the value of Λ21 is higher than Λ12, which demonstrates that the adsorbed molecules of CO2 provide strong interactions on the molecules of CH4. This phenomenon could be also found in the CH4 (1) − C2H6 (2) system and the CO2 (1) − C2H6 (2) system, which may explain why the experimental data in Figure 4 are higher than the prediction results of the EL equation and the IAST model. Therefore, even on the homogeneous surface, these binary mixtures perform nonideal behavior. It means the nonideality of

(11)

where γi is the activity coefficient accounting for the adsorbed phase nonideality. The difference between the IAST model and the RAST model is the introduction of the activity coefficients in the RAST model. The activity coefficients are a function of the composition of the adsorbed phase and the spreading pressure. Presently, no models are available to predict activity coefficients for the adsorbate mixtures. On the basis of our binary experimental adsorption data and the method proposed by Vaart et al., the spreading pressure of the mixture could be evaluated using the cubic spline interpolation to express the relationship between the total amount adsorbed and the equilibrium pressure.11 Thus, the activity coefficients could be 2586

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Table 7. Wilson Interaction Parameters for Binary Adsorption Systems adsorbed phasea

bulk liquid

CH4 (1)−CO2 (2) Λ12 Λ21

0.15 2.57

Λ12 Λ21

0.14 2.48

Λ12 Λ21

0.44 1.64

0.40b 0.02b CH4 (1)−C2H6 (2) 1.64c 0.12c CO2 (1)−C2H6 (2) 1.08d 0.48d

a

Calculated in this work. bCalculated from data given by Mraw et al.18 Calculated from data given by Wichterle et al.19 dCalculated from data given by Fredenslund et al.20

c

In addition, adsorption of a binary mixture C2H6−C2H4 on NaETS-10 demonstrated that the experimental data of C2H6 is higher than the prediction of the IAST model.16 In this system, C2H6 is the lighter component because C2H4 adsorbed more strongly than C2H6. For adsorption of a ternary mixture CH4− C2H6−C2H4 on BPL activated carbon, the dual-site Langmuir (DPL) model also provided lower predicted values for CH4 in the high pressure range, which is the lightest component.17

Figure 6. Experimental and fitted Wilson equation activity coefficients for CH4 (1)−C2H6 (2) adsorbate mixtures at 293.2 K. Solid symbols: γ1 for CH4; open symbols: γ2 for C2H6. Square: π* = 0.20 mol/kg; circle: π* = 0.25 mol/kg; triangle: π* = 0.30 mol/kg; diamond: π* = 0.35 mol/kg.

4. CONCLUSIONS Adsorption equilibria for binary gas mixtures on GCB STH-2 were measured using the open flow method in this work, including CH4−CO2, CH4−C2H6, and CO2−C2H6. Applications of the EL equation and the IAST model demonstrate that the adsorbed mixtures show nonideality to some extent. Because the GCB STH-2 does not have an energetically heterogeneous surface, the nonideality should be dominantly related to adsorbed phase nonuniformity other than adsorption energy heterogeneity. The RAST model with the Wilson equation is used to analyze the adsorption equilibrium data. The study shows that the properties of the adsorbed phase are different from the bulk liquid phase. The existence of the heavier component in adsorption process could improve the adsorption of the lighter component. More physical interpretation should be made to relate the properties of the adsorbed phase with the bulk liquid phase.

■

Figure 7. Experimental and fitted Wilson equation activity coefficients for CO2 (1)−C2H6 (2) adsorbate mixtures at 293.2 K. Solid symbols: γ1 for CO2; open symbols: γ2 for C2H6. Square: π* = 0.30 mol/kg; circle: π* = 0.40 mol/kg; up-pointing triangle: π* = 0.50 mol/kg; down-pointing triangle: π* = 0.60 mol/kg; diamond: π* = 0.70 mol/kg; left-pointing triangle: π* = 0.80 mol/kg.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: 86/21/65 98 10 97.

■

ACKNOWLEDGMENTS This project was supported by the National Natural Science Foundation of China (20506019).

■

adsorbed phase is an inherent effect on the prediction of multicomponent adsorption equilibria. If the adsorbent has an energetically heterogeneous surface, the properties of adsorbed phase are more complicated.11 According to the definition of binary interaction parameters Λ12 and Λ21, the change of Λ12 and Λ21 perhaps results from the change between molecular lateral interactions, because the two-dimensional state of molecules on the solid surface is different from that in the bulk liquid state. It seems that the adsorption of the heavier component would benefit the lighter component adsorption, which is consistent with the investigation of CH4−C2H6 on activated carbon in the literature.8,15

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