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Study of Binary Adsorption Equilibrium of Hydrocarbons in Activated Carbon Using Micropore Size Distribution 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 December 9, 1999. In Final Form: March 6, 2000 Adsorption equilibria of gases on Norit activated carbon were measured using a differential adsorber bed rig. The binary gas mixtures between three hydrocarbon gases, i.e., methane, ethane, and propane, were employed in the experiment as adsorbates. The experimental equilibrium data were used to examine the predictive capability of the multicomponent equilibrium model, which utilizes the concept of micropore size distribution and Lennard-Jones potential theory to describe the adsorption energetic heterogeneity on activated carbon. The effects of the minimum size of pores accessible to adsorbates and the constraint in the saturation adsorption capacity of the extended Langmuir equation on the prediction performance are investigated within the model.
Introduction Adsorption equilibrium is the key information for the design of practical separation processes based on adsorption mechanisms. A number of reviews on adsorption equilibrium are available in the literature.1-7 However, it still remains an important and challenging issue nowadays to predict the multicomponent adsorption equilibria using the information from the related pure component systems, especially when the system presents strong adsorption energetic heterogeneity. The prediction of multicomponent equilibria plays an important role in the adsorption kinetics as well. As has been indicated in the study of Hu and Do,8 a small deviation in the prediction of adsorption equilibria can cause a large error in the simulation of adsorption kinetics for a system containing more than one species. Strong adsorption energetic heterogeneity is commonly observed on such adsorbents as activated carbon and dictates the overall adsorption equilibria of the system. A number of models have been proposed to address the role of energetic heterogeneity in adsorption equilibria. Generally the adsorbent is treated as being patchwise, i.e., a combination of sites (or volumes) having different energies,3,6,9 selectivities,7 or affinities,10 * To whom all correspondence should be addressed. E-mail:
[email protected]. Tel: +852 23587134. Fax: +852 23580054. (1) House, W. A. Adsorption on Heterogeneous Surfaces. Colloid Sci. 1983, 4, 1-58. (2) Ruthven, D. M. Principles of Adsorption and Adsorption Processes; Wiley: New York, 1984. (3) Yang, R. T. Gas Separation by Adsorption Process; Butterworths: Boston, MA, 1987. (4) Rudzinski, W.; Everett, D. H. Adsorption of Gases on Heterogeneous Surfaces; Academic Press: New York, 1992. (5) Jaroniec, M.; Madey, R. Physical Adsorption on Heterogeneous Solids; Elsevier: Amsterdam, 1988. (6) Sircar, S.; Myers, A. L. Equilibrium Adsorption of Gases and Liquids on Heterogeneous AdsorbentssA Practical Viewpoint. Surf. Sci. 1988, 205, 353-386. (7) Sircar, S. Role of Adsorbent Heterogeneity on Mixed Gas Adsorption. Ind. Eng. Chem. Res. 1991, 30, 1032-1309. (8) 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. (9) Ross, S.; Olivier, J. P. On Physical Adsorption. XII. The Adsorption Isotherm and the Adsorptive Energy Distribution of Solids. J. Phys. Chem. 1961, 65, 608-615. (10) Gusev, Y. N.; O’Brien, J. A.; Jensen, C. J.; Seaton, N. A. Theory for Multicomponent Adsorption Equilibrium: Multispace Adsorption Model. AIChE J. 1996, 42, 2773.
etc. For physical adsorption processes on activated carbons, this energetic heterogeneity mainly arises from the dispersive interaction between the adsorbate molecules and the slit-shaped micropores and, as a result, the size distribution of the slit-shaped micropores (MPSD) dictates the overall adsorption equilibria on the adsorbent. This mechanism has been used in a number of research studies to investigate the adsorption process on activated carbon.11-13 Jaggiello and Schwarz14,15 studied the effect of MPSD on pure component adsorption equilibrium of a number of species on activated carbons with this methodology. Hu and co-workers16 applied this methodology to sorption kinetics of pure component systems with good success. Later, they further extended this model to the adsorption equilibria of multicomponent systems,17-19 and in doing so the size exclusion phenomenon and an adsorbate-pore interaction scheme are introduced. Recently, Wang and Do20 modified this model on the basis of the kinetic theory of gases and proposed that this MPSD should take into account the equilibrium information of (11) Gubbins, K. E. Theory and Simulation of Adsorption in Micropores. In Physical Adsorption: Experiment, Theory and Applications; Fraissard, J., Ed.; Kluwer Academic Publishers: Norwell, MA, 1997; pp 65-103. (12) McCallum, C. L.; Bandosz, T. J.; McGrother, S. C.; Mu¨ller, E. A.; Gubbins, K. E. A Molecular Model for Adsorption of Water on Activated Carbon: Comparison of Simulation and Experiment. Langmuir 1999, 15, 533-544. (13) Kaneko, K. Specific Intermolecular Structures of Gases Confined in Carbon Nanospace. Carbon 2000, 38, 287-303. (14) 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. (15) Jagiello, J.; Schwarz, J. A. Relationship between Energetic and Structural Heterogeneity of Microporous Carbons Determined on the Basis of Adsorption Potentials in Model Micropores. Langmuir 1993, 9, 2513-2517. (16) 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. (17) 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: Norwell, MA, 1996; pp 385-392. (18) Hu, X. Multicomponent Adsorption Equilibrium of Gases in Zeolite: Effect of Pore Size Distribution. Chem. Eng. Commun. 1999, 174, 201-214. (19) Qiao, S.; Wang, K.; Hu, X. Using Local IAST with Micropore Size Distribution To Predict Multicomponent Adsorption Equilibrium of Gases in Activated Carbon. Langmuir 2000, 16, 1292-1298.
10.1021/la991613w CCC: $19.00 © 2000 American Chemical Society Published on Web 05/03/2000
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several adsorbates as well as their molecular properties simultaneously. Since an extended Langmuir equation is used as the local isotherm for multicomponent systems, the thermodynamic requirement of the extended Langmuir model deserves some attention. Theoretically, the saturation capacities of different species in the EL isotherm should be the same to meet the thermodynamic consistency. However, the predictability of the model can be possibly discounted with such a constraint.21 The other parameter that incurs some uncertainty in the model is the choice of the minimum pore size accessible to the adsorbate molecule, which has been proved to be less significant for the equilibrium of pure component systems.15 For a multicomponent system, however, this parameter deserves some further study since it determines the accessibility of adsorbates in the microporous network and the matching energies among different species in the adsorbed phase as well. The experimental technique for the measurement of multicomponent adsorption equilibria is also an important issue. In the past, gravimetric method, volumetric method, or the combination of the two has been mainly used in practice.3,22 In this study, however, a differential adsorber bed (DAB) rig is used instead. The DAB rig measures the adsorbed-phase concentration directly, and the experimental conditions in such a rig closely parallel those in measuring sorption kinetics. Since DAB rigs were mainly used to measure adsorption kinetic data, the validation of the equilibrium relation in such a rig will serve as a good support for the study of kinetic data.
The surface heterogeneity of an activated carbon arises from the size distribution of the slit-shaped micropores. For the adsorption of multicomponent systems on an activated carbon, the local adsorption isotherm of species k at a given adsorption site (micropore) is assumed to follow the extended Langmuir equation, i.e.
10
σsk 4 + z 2 σsk 5 2r - z
-
10
-
σsk 2r - z
)} 4
(1c)
where r is the pore half-width, z is the distance between / the the adsorbate molecule and one of the pore walls, sk potential well depth, and σsk is the Lennard-Jones collision diameter determined from the Lorentz-Berthelot rule. If the micropore size distribution of activated carbon follows some kind of distribution function, for example, the nonnegative γ distribution
f(r) )
qv+1rve-qr Γ(v + 1)
(2)
then the observed isotherm on the adsorbent will be the integral of the local adsorption isotherm over the pore size distribution range, i.e. ∞
b0(k)eE(k,r)/RTCp(k)
min(k)
NC
∫r
1+
×
ξ(j) b0(j)eE(j,r)/RTCp(j) ∑ j)1 f(r) dr (3a)
where
ξ(j) )
b0(k)eE(k,r)/RTCp(k)
1+
{( ) ( ) ( ) (
σ * 5 2 sk up(k, z) ) sk 3 5 z
Cµ(k) ) Cµs(k)
Theory
Cµ(k, r) ) Cµs(k)
Equation 1b is derived from the kinetic theory of gases.23 The local adsorbate-adsorbent interaction energy, E(r), is taken as the negative of adsorption potential minimum in the micropore.14 Here, the model micropore is assumed to be contained in two parallel graphite lattice layers with infinite extent, for which the adsorption potential of an adsorbate molecule takes the form of the 10-4 potential24
{
1 if r > rmin(j) 0 if rmin(k) < r < rmin(j)
(3b)
NC
b0(j)eE(j,r)/RTCp(j) ∑ j)1 (k ) 1, 2, ..., NC) (1a)
where Cµ(k, r) is the adsorbed-phase concentration, Cp the gas-phase concentration, R the gas constant, T the temperature, NC the number of components in the system, b0 the adsorption affinity constant at zero energy level, and E(k,r) the adsorption energy. For a physical adsorption process of gas mixtures, this parameter relates different species via the following expression
b0 )
β
xMkT
(1b)
where M is the molecular weight and β is the affinity parameter specific to the structure of the adsorbent. (20) 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. (21) 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. (22) Keller, J. U.; Staudt, R.; Tomalla, M. Volume-Gravimetric Measurements of Binary Gas Adsorption Equilibria. Ber. Bunsen-Ges. Phy. Chem. 1992, 96, 28-32.
where rmin is the minimum half-width of pore accessible to the adsorbate (the pore cutoff). This parameter is important since it determines the accessibility of each species in the microporous network of the adsorbent and affects the matching energies between different species in the adsorbed phase. Different criteria have been used in the literature to choose this value: (1) pores in which the adsorption potential is zero;14 (2) pores in which the adsorption potential is the same as that on a flat surface,20 and (3) pores in which the “internal diameter” equals the diameter of the adsorbate molecule.17 Jagiello and Schwarz15 showed that the choice of this “cutoff” does not play a significant role in pure component adsorption equilibrium. For multicomponent systems, however, this conclusion may not be valid owing to the reason mentioned before. Two scenarios of pore cutoff are investigated in this study: (1) the pores with the halfwidth of 0.858σsk, corresponding to the pores in which the adsorption potential is approximately zero with the 10-4 potential, and (2) the pores with the half-width of σsk, corresponding to the pores of which the “chemical diam(23) Do, D. D.; Wang, K. Predictions of Adsorption Equilibria of Nonpolar Hydrocarbons onto Activated Carbon. Langmuir 1998, 14, 7271-7277. (24) 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.
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Table 1. Physical Properties of Norit Activated Carbon particle bulk density total porosity macropore porosity (>6 × 10-9 m) micropore porosity (
