2630
Langmuir 1993,9, 2530-2536
Effect of Surface Energetic Heterogeneity on the Kinetics of Adsorption of Gases in Microporous Activated Carbon Xijun Hu and Duong D. Do* Department of Chemical Engineering, University of Queensland, Brisbane, Queensland 4072, Australia Received July 20, 1992. I n Final Form: October 26, 1992 A model allowing for surfaceenergeticheterogeneityis presented to describethe ademption and desorption kinetics of gaseous adsorbates in large microporous particles. The effects of surface energeticheterogeneity on both sorption kinetics and equilibrium (rather than on equilibrium only) are studied. Parameters extracted from single component fittings are used to predict the multicomponent sorption dynamics. Singleand multicomponentexperimentaldata of sorptiondynamics of ethane and propane in Ajax activated carbon, which are obtained by using a differential adsorption bed, are used to demonstrate the potential of the proposed model. It is found that the role of energetic heterogeneity is not important in the model fittings of adsorption kinetics of single component, but it plays a vital role in the predictions of desorption kinetics of singlespecies and adsorption and desorption processes of multicomponentgases in microporous particles. This finding has a far reaching consequence as all adsorption systems of industrial interest involve interaction of many adsorbates.
Introduction The surface energetic heterogeneity concept has long been recognized in the measurement of adsorption equilibrium isotherms of gases.14 In the attempts to predict the multicomponent equilibria using single component isotherm information for heterogeneous systems, various models have appeared in literatures. The approach proposed by Myers7 requires an iterative solution to determine the mixed adsorption equilibrium after the adsorption isotherms for single species on a heterogeneous surface are obtained. Another methodology is to assume a local multicomponent isotherm at a single site and integrate it over the full site energy distribution.8~~In this paper, the heterogeneous extended Langmuir model proposed by Kapoor et al.,l0 which computes the gas mixture equilibrium by using an extended Langmuir isotherm on a patch of surface and then integrates it over a uniform energy distribution, is used to describe the multicomponent equilibrium of ethane and propane in Ajax activated carbon. The saturation adsorption capacities of ethane and propane in Ajax carbon are forced to be identical in the single component isotherm fittings in order to meet the thermodynamic consistency. More recently, the effect of surface energetic heterogeneity on the surface diffusion is also studied but
* Author to whom all correspondence should be addressed.
(1)Roginski, S. S. Adsorption and Catalysis on Heterogeneous Surfaces; Academy of Sciences of USSR Moscow, 1984 (in Russian). (2) Rogineki, S. S. Adsorption und Katalyse an Homogenen Oberflachen; Akademie: Berlin, 1958. (3) Ross,S.;Olivier, J. P.OnPhyaicalAdsorption. XII. The Adsorption Isotherm and the Adsorptive Energy Distribution of Solids. J. Phys. Chem. 1961,65 (4), 608-615. (4) Misra, D. N. New Adsorption Isotherm for Heterogeneous Studies. J. Chem. Phys. 1970,52 (111, 5499-5501. (5) Sircar,S.New Adeorption Isotherm for EnergeticallyHeterogeneous Adsorbenta. J. Colloid Interface Sci. 1984, 98 (2), 3OE-318. (6) Sircar, S.;Myere, A. L. Equilibrium Adsorptionof Gasesand Liquids on Heterogeneous Adsorbenta-A Practical Viewpoint. Surf. Sei. 1988, 205,353-386. (7) Myers, A. L. Adsorption of Pure Gases and Their Mixtures on Heterogeneous Surfaces. In Fundamentab of Adsorption; Myers, A. L., Belfort, G.,Me.; Engineering Foundation: New York, 19&4;pp 365-381. (8) Valenzuela, D. P.; Myers, A. L.; Talu, 0.;Zwiebel, I. Adsorption of Gas Mixtures: Effect of Energetic Heterogeneity. AZChEJ. 1988,34(3), 397-402. (9) Moon, H.; Tien, C. Adsorption of Gas Mixtures on Adsorbenta with Heterogeneous Surfaces. Chem. Eng. Sci. 1988,43 (ll),2967-2980. (10) Kapoor, A.; Ritter, J. A.; Yang, R. T. An Extended Langmuir Model for Adsorption of Gas Mixtures on Heterogeneous Surfaces. Langmuir 1990,6 (3), 660-664.
restricted to steady state.11-17 The role of energy distribution in the transient sorption dynamics was recently studied by Do and Hula and Hu et al.lg for singlecomponent systems. The necessity of having a mathematical model to predict the multicomponent sorption dynamics from information of single species is obvious because of the many possible combinations of multicomponent systems and of the fact that all industrial adsorption processes involve more than one adsorbate. In this paper, we propose a heterogeneous macropore and surface diffusion (HMSD) model to describe the multicomponent adsorption dynamics of gases in a large microporous particle. The diffusion of adsorbed species is calculated using a chemicalpotential gradient driving force expression on a single patch and integrating it over an energy distribution. This model provides better predictions than the macropore and surface diffusion (MSD) model proposed earlier by Hu and Do28 on the multicomponent dynamic data using only information of single component mass transfer and equilibria.
Theory A large heterogeneous microporous particle is exposed to a constant bulk concentration environment which contains NC adsorbate species. The patchwise model is (11) Okazaki, M.; Tamon, H.; Toei, R. Interpretation of Surface Flow Phenomenon of Adsorbed Gases by Hopping Model. AIChE J. 1981,27 (21, 262-270. (12) Tamon, H.; Okazaki, M.; Toei, R. Flow Mechanism of Adsorbate through Porous Media in Presence of Capillary Condeneation. AIChE J. 1981,27 (2), 271-277. (13) Zgrablich, G.;Pereyra, V.; P o d , M.; Marchese, J. Connectivity Effects for Surface Diffusion of Adsorbed Gases. AZChE J. 1986,92 (7), 1158-1168. (14) Horas, J. A.; Saitua, H. A.; Marchese, J. Surface Diffusion of Adsorbed Gases on an Energetically Heterogeneous Porous Solid. J. Colloid Interface Sci. 1988, 126 (2), 421-431. (15) Seidel, A.; Carl, P. The Concentration Dependence of Surface Diffusion for Adsorption on Energetically Heterogeneous Adsorbenta. Chem. Eng. Sci. 1989,44 (l), 189-194. (16) Kapoor, A.; Yang, R. T. Surface Diffusion on Energetically Heterogeneous Surfaces. AZChE J. 1 9 8 9 , s (lo), 1735-1738. (17)Kapoor, A.; Yang, R. T. Surface Diffusion on Energetically Heterogeneous Surfaces-An Effective Medium Approximation Approach. Chem. Eng. Sci. 1990,45 (ll),3261-3270. (18)Do, D. D.; Hu, X.An Energy Distributed Model for Adsorption Kinetics in Large Heterogeneous Microporous Particles. Chem. Eng. Sci., in press. (19) Hu, X.;Rao, G.N.;Do, D. D. Effect of Energy Distribution on Sorption Kinetics in Bidispersed Particles. AZChE J.,in press.
0743-7463/93/2409-2530$04.00/0 0 1993 American Chemical Society
Effects of Surface Energetic Heterogeneity
Langmuir, Vol. 9, No. 10,1993 2531
used to describe the heterogeneity of the surface. The assumptions in the model development are as follows: (1) The system is isothermal. (2) The particle is large enough so that the mass transfer resistance is in the particle coordinate. (3) Both free and adsorbed species diffuse inside the particle. (4) The particle surface is heterogeneous in the sense that there is an interaction energy distribution between adsorbate and adsorbent. ( 5 ) The pore diffusivity, film mass transfer coefficient, and the surface diffusivity at zero surface loading are constant.
Local Adsorption Isotherm and Energy Distribution. The local adsorption isotherm for a given’sitewith an adsorption energy E ( k ) is assumed to follow the
The Local Flux of the Adsorbed Species. By using the chemical potential gradient as the driving force of the diffusion of the adsorbedspecies,we can write the diffusion flux of the adsorbed species k at the energy level E(k) as
or in terms of the adsorbed concentration gradients
J,[kB(k)l = - D , , [ k B C,[kB(k)l NC
(k)1
extended Langmuir equation of the following form:
b[kB(k)lC,(k) C,[kB(k)l = C,(k)
NC
(1)
where C, is the gas phase concentration, C , is the maximum adsorbed phase concentration, C,[k(E(k)l and b[k&(k)] are the adsorbed phase concentration and the affinity for adsorbate k for a given site of energy E @ ) , respectively, and the affinityis correlated to the interaction energy by the following equation:
with bo being the affinity at the zero energy level or at the infinite temperature. Let the energy distribution in the adsorbed phase be F [ k J ( k ) ] ; the macroscopically observed isotherm at a given gas phase concentration C,(k) (k = 1, NC)is
C,,,(k)
=
C,W
c 1-1
aCp(k) dC,b’BO’)l (8)
a c , l j ~ ~ ’ ) i ar
with D,[k$(k)l having the following functional dependence on temperature
and D,&) being the surface diffusivity of zero energy at zero loading of species k. Mass Balance Equations. The mass balance equation in the particle phase is
a(,J)=J,rkAk)lF[kB(k)l ar dE(k)) (10) where s it the particle shape factor, with a value of 0, 1, or 2 being for slab, cylinder, or sphere, respectively, CM is the macropore porosity, and Jpis the pore flux and defined as20
j=l
where the energy distribution function satisfies the following equation:
J)=F[kB(k)I d E ( k ) = 1
(4)
In this paper we will only discuss the uniform energy distribution which has the following form
where D , is the pore diffusivity based on the pore crosssectional area. In the LHS of Equation (lo), the first term is the accumulation of the free species and the second term is that of the adsorbed species.21*22In the right-hand side of eq 10, the first term is the diffusion contributed by the free species and the second term is that contributed by the adsorbed species on a surface having pachwise topography. For arandom topography,the effectivemedium approach of Kapoor and Yangl7 is more suitable. The boundary conditions of the above mass balance equation are
and F[k,E(k)] = 0 elsewhere. By assuming that the ordering of the energy sites from low to high is the same for different adsorbates and the cumulative energy distribution function is the same for all species in the mixture? the correlation of energiesof different speciesfor a uniform energy distribution islo
where the whole energy distribution region of one species is matched to that of another species. The extended Langmuir equation has been wed for the local adsorption isotherm (eq 1); hence, it is required for different species to have the same maximum adsorption capacities in order to be thermodynamically consistent.
(20) Ruthven, D.M.Principles of Adsorption and Adsorption R o cesses; Wiley New York, 1984. (21) Aharoni, C.; Ungarish, M. Kinetics of Activated Chehrption. Part 2. TheoreticalModels. J. Chem. SOC.,Faraday Tram 1977,73 (3), 456-464. (22) Crickmore,P. J.; Wojciechowski, B. W. Kinetica of Adsorption on Energetically Heterogeneous Surfaces. J. Chem. Soc., Faraday Trom 1977, 73,1216-1223.
Hu and Do Table I. Definitions of Nondimenrional Variables and Parameters e(k) =
$$
flk,e(k)l = F[kJ(k)IRT;
e(k) = ce(k)f[k,e(k)l de(k)
Solution Methods The model equationsare cast into nondimensionalforms by defining the nondimensionalvariables and parameters as tabulated in Table I. The resulting nondimensional mass balance equation is
(15) and the boundary conditions (eqs 12 and 13) become
ay,w ax f[k,e(k)l de&) = Bi[Yb(k)- Yp(k)l (17) The nondimensionalequations (eqs 15-17) are numerically solved by using a combination of the orthogonal collocation technique23and a differential-algebraic equation solver. The integrals involving the energy distributions are evaluated by using the RADAU q u a d r a t ~ r e . ~ ~
Experiments The adsorbent used in this study is Ajax activated carbon Type 976 supplied by Ajax Chemical Co., Australia, as '/le in. diameter cylindrical extrudates. The structural properties of Ajax carbon and the preparation of slab particles are available elsewhereau3 The adsorption equilibria of ethane and propane in Ajax activated carbon were measured via a high accuracy volumetric adsorption isotherm measurement rig. The dynamic adsorption data of ethane and propane (single and binary) onto Ajax carbon were obtained using a differential adsorption bed (DAB). The operational procedures of single component adsorption dynamicscan be found in Hu et al.18 The binary dynamic experiments are done in the similar way except that two components are now simultaneously adsorbed onto the Ajax activated carbon. The isothermal condition is justified by the high flow rate of the adsorbates and from a thermocouple inserted inside the adsorber.
Results and Discussions Firstly, the adsorption equilibrium data of ethane and propane in Ajax activated carbon were collected for three temperatures, 10,30,and 60 "C,which are shown in Figure (23) Villadsen, J.; Michelsen, M. L. Solution of Partial Differential Equation Models by Polynomial Approximation; Prentice-Hall: En-
glewood Cliffs, NJ, 1978. (24) Gray, P. G.; Do, D. D. Adsorption and Desorption of Gaseous Sorbates on a Bidispereed Particle with Freundlich Isotherm. 11. Experimental Study of Sulphur Dioxide Sorption on Activated Carbon Particles. Gas Sep. Purif. 1989, 3, 201-208. (26) Do, D. D.; Hu, X.; Mayfield, P. L. J. Multicomponent Adsorption of Ethane,n-butane and n-Pentanein Activated Carbon. Gas Sep. Purif. 1991, 5, 35-48.
1. Also plotted in Figure 1 are the model fittings of the Langmuir-Uniform distribution and Langmuir equations. When fitting the data to the Langmuir-Uniform distribution equation, the parameters E&, E-, and bo were set to be temperature independent but species dependent, while the saturation parameter, C, was set to the same for ethane and propane but temperature dependent. The reason for this is that the identicalvalues of C, for different species are required for the local extended Langmuir isotherm to be thermodynamically consistent. Since the molecular sizes of ethane and propane are close to each other, this assumption appears to be reasonable. From Figure 1, we can see that the agreement between the Langmuil-Uniform distribution equation and the experimental data is very good, even when the above mentioned
Effects of Surface Energetic Heterogeneity
Langmuir, Vol. 9, No. 10, 1993 2533 1.0 0.6 0.6
0.4
0.0' 0
0
20
40
80
60
5% e 10% v 20% 0
1yo
0.2
"
"
I
'
"
500
" '
"
'
1000
!
"
1500
100 120
0
id E
0.. 0.
o
"
'
'
1
500
---"
"
1
v 10% '
"
"
1000
1500
1.0 0.6
0.6 0 " ' " " " " " ~ 0 20 40 60 80
0.4
100 120
Figure 1. Effect of energy distribution on the adsorption equilibrium isotherm of ethane and propane in an Ajax activated Langmuircarbon: (a)ethane/carbon, (b)propane/carbon;(-) Uniform distribution isotherm, (- - -) Langmuir isotherm. Table 11. Isotherm Parameters for Ethane/Ajax Activated Carbon Langmuir-Uniform distribution Langmuir isotherm (Unilan) isotherm t-P
c,
("C) (InnoVms) 10 13.0 30 13.0 60 13.4 bo (Wa-1) Emin (kJ/mol) E- (kJ/mol)
b (Wa-1) 2.20 X lp 1.31 X 10-S 6.77 X lo-' 8.47 x 6.26 30.76
s
5.20 4.86 4.42 lo-'
cw (kmoUm3)
b (ea-')
5.49 5.00 4.58
0.0516 0.0320 0.0167
Table 111. Isotherm Parameters for Propane/Ajax
Activated Carbon LangmukUniform Distribution Isotherm (Unilan)
10 13.0 30 13.0 60 13.4 bo (Wa-1) Emin (kJ/mol) E- (kJ/mol)
1.70 X lo" 9.08 9.34 X lo-' 8.48 4.35 X lo-' 7.72 1.93 X lo-' 0.0 42.75
0
Langmuir isotherm
5.00 4.69 4.36
0.470 0.217 0.0863
restrictions are applied. The Langmuir equation cannot describe the equilibria of propanelcarbon adsorption data well, although it can reasonably fit the experimental data of ethanelcarbon. The adsorption isotherm parameters of ethane and propane in Ajax activated carbon are listed in Tables I1and 111. A little surprising is that the saturation capacity (C,) of the Unilan isotherm at 60 "C is a bit larger than that at 10 or 30 "C. This could be due to the fact that no data at higher pressure (>130 P a ) are available, which are needed to accurately determine the maximum adsorption capacity. A similar temperature trend of the saturation capacity is also seen in work of Kapoor and Yang16 and Moon and Tien.g Secondly the single component dynamic data were used to extract the kinetic parameters of ethane and propane
5%
e 10% v 20%
0.2
Pressure (kPa)
0.0"""""""""'"""' 0 200 400 600
600
11
1000
Time ( S e c o n d s ) Figure 2. Effect of energy distribution on the sorption dynamics of ethane onto an Ajax activated carbon of 4.4 mm full length HMSD slabs at 1 atm: (a) 10 "C, (b) 30 "C, (c) 60 O C ; (-1 model, (- - -) MSD model.
adsorption in Ajax carbon. A slab particle of 4 mm full length has been shown to be under macropore and surface diffusion contro1.26a For the Ajax carbon, a macropore tortuosity of eight has been obtained for the macropore and surface diffusion mechanism^.^^^^^ In this paper, Ajax carbon particles of 4.4 mm full length slab were used for the kinetic studies and the tortuosity of eight was used to calculatethe pore diffusivities of ethane and propane from the combined molecular and Knudsen diffusivities. Therefore, the only fitting parameter in the model is the zero coverage surface diffusivity at zero energy level. The ratio of the surface activation energy to the heat of adsorption, a , is set to be 0.5 for the adsorption of ethane and propane in Ajax carbon. Figure 2 shows the adsorption dynamics of ethane onto 4.4 mm full length slab particles of Ajax activated carbon at three bulk concentrations (5, 10, and 20%) and three temperatures (10,30, and 60 "C). The total pressure is 1atm. The model fittings (solid lines) with an extracted zero coverage surface diffusivity at zero energy level, D,o, of 7.02 X lV7 m2/s are in good agreement with the experimental data (symbols) for all three temperatures. For comparisons, the MSD model2*fittings using a Unilan equation7 are also plotted in Figure 2 as dashed lines. Although the MSD model also fib the data well, the HMSD model has an advantage that only one parameter of zero coverage surface diffusivity at zero energy level is needed for different temperatures, while the MSD model requires different zero coverage diffusivities for different temper~
~~~~
(26) Gray, P. G.; Do, D. D. Adsorption and Deeorption Dynamics of Sulphur Dioxide on a Single Large Activated Carbon Particle. Chem Eng. Commun. 1990,96, 141-164. (27) Mayfield, P. L. J. Fundamental Investigations into Adsorption Kinetica of Light Hydrocarbons onto Activated Carbon. Ph.D. Thesis, University of Queensland, Australia, 1990. (28) Hu, X.; Do, D. D. Multicomponent Adsorption Kinetics of Hydrocarbons onto Activated Carbon: Effect of Adsorption Equilibrium Equations. Chem. Eng. Sei. 1992,47 (7), 1716-1726.
Hu and Do
2634 Langmuir, Vol. 9,No. 10,1993
Table IV. Dynamic Parametere of Ethane/Ajax Activated Carbon temp ( O C ) D. (W m2/s) D, (lo"m2/s) MSD model 10 1.51 2.58 30 60 10 30 60
HMSD model a Value
1.68 1.96 1.51 1.68 1.96
3.41 6.26
.
u w'.,
00.0 .5
702O
i
reported is Da and a = 0.5.
0.4 0.2
r
0 . 0 r
'
"
0
I
10% 0 52 0% v % 0
'
"
500
" '
" '
"
"
1500
1000
'
i'
: w k
0.0
L
o
2000
1000
3000
2000 1.0
d
0.6
0.5
le d -
0.4
3
0.2
;1:
0.0'.
----TGj ---___
0
i!
0
% i
"
"
"
500
"
I
'
"
"
1000
"
1500
"
"
0
'
0.8
10% 0 520% v % 0
0.2
o.o~"""'""""""' 0
500
1000
1500
1
2000
Time (Seconds)
Figure 3. Effect of energydistribution on the sorption dynamics of propane onto an Ajax activated carbon of 4.4 mm full length HMSD slabs at 1 atm: (a) 10 O C , (b) 30 O C , (c) 60 O C ; (-) model, (- - -) MSD model.
Table V. Dynamic Parameters of Propane/Ajax Activated Carbon temp ( O C ) D, (10-9m2/s) D, (les m2/s) MSD model 10 1.20 0.789 30 60 HMSD model
10
30 60 a Value
1.30 1.56 1.20 1.30 1.56
~
"
1000
'
"
'
'
"
2000
3000
Figure 4. Effect of energy distribution on the binary adsorption dynamics of ethane and propane onto an Ajax activated carbon of 4.4 mm full length slabs at 10 O C , 1atm: (a) 5% ethane and 5% propane, (b) 10% ethane and 5% propane, (c) 20% ethane HMSD model, (- - -) MSD model. and 5% propane; (-)
1.0
0.4
'
Time ( S e c o n d s )
2000
0.6
~
0.928 1.75 1340"
reported is Dfl and a = 0.5.
atures. The surface diffusivity extracted from adsorption data is then used to predict the desorption dynamics of 10% ethane in Ajax carbon at 30 "C, 1atm which is plotted in Figure 2b. Since the energy distribution is not important in the adsorption equilibrium of ethane/carbon (Figure la),both models can equally predict the desorption kinetics well. The dynamic parameters of ethane adsorption in Ajax activated carbon are tabulated in Table IV. The adsorption dynamics of propane (5,10,and 20% ) onto Ajax activated carbon of 4.4 mm full length slab particles at three temperatures (10, 30, and 60 "C) are shown in Figure 3. Again both models fit the experimental data well with the dynamic parameters listed in Table V. However, the prediction of the MSD model on the desorption dynamics of 10% propane in 4.4 mm slabs of Ajax carbon is below the experimental data, which are,
however, correctly predicted by the HMSD model (Figure 3b). Because the energy distribution is important in the adsorption equilibrium of propane/carbon (Figure lb), the role of the surface energetic heterogeneity in the desorption dynamics is now clearly seen. From Figures 2 and 3, it is seen that the external bulk concentration dependency of the single component adsorption dynamics is less significant at a higher temperature. It is also observed that the MSD model is less sensitive to the bulk concentrationsthan the HMSD model. This is consistent with the observations of Seidel and Carl,lSwhere they used the surface energeticheterogeneity to explain the concentration dependence of surface diffusion. Having obtained the adsorption equilibrium and mass transfer parameters of single component systems, we can now use these parameters to predict the binary adsorption dynamics. Figure 4 shows the simultaneous adsorption kinetics of 5 % propane together with different concentrations of ethane (5, 10, and 20%) onto 4.4 mm slab particles of Ajax activated carbon at 10 "C,1 atm. The predictions of the HMSD model (solid lines) are in very good agreement with the experimental data. The results of the MSD model prediction, which uses the ideal adsorption solution theory (IAST),aand a Unilan equation for single component isotherm to compute the multicomponent adsorption equilibrium, are also plotted in Figure 4 as dashed lines. Since the surface energetic heterogeneity is very significant in the adsorption equilibrium of propanel carbon at 10 "C,the MSD model fails to accurately predict the binary adsorption dynamics. The great potential of the HMSD model as a mathematical tool to study the multicomponent adsorption kinetics in a large particle is clearly revealed here. (29)Myers, A. L.;Prausnitz, Thermodynamics of Mixed-gaa Adsorption. AlChE J. 1965, 11 (l), 121-127.
Langmuir, Vol. 9, No.10,1993 2535
Effects of Surface Energetic Heterogeneity
1.5 1.0
L I 4
0.5 nn
0.0
V."
500
0
1000
2000
1500
-
0 ld
2
1000 1500 2000 2500 ,.,,, , ,...,, ,,
500
1.5 r . ,
.,,
.,
, , , ,
a
3
1.0
4
' 0.0'.
"
0 2.0
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"
0
'
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1
o.or,
'
I
"
1000
"
'
"
'
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,' 2000
0
2
0.0
L
0
500
1000 1500 2 0 0 0 2500
0
500
1000 1 5 0 0 2000 2500
,
"
"
"
500
'
"
"
1000
"
'
"
1500
'
"
0.0
2000
Time (Seconds)
Figure 5. Effect of energy distributionon the binary adsorption dynamics of ethane and propane onto an Ajax activated carbon of 4.4 mm full length slabs at 30 O C , 1 atm: (a) 10%ethane and 10% propane, (b) 5% ethane and 10%propane, (c) 5% ethane HMSD model, (- - -) MSD model. and 20% propane; (-) The proposed model is further tested with the binary adsorption dynamics of ethane and proposed in Ajax carbon of 4.4 mm slabs at 30 OC under different concentration combinations, which are shown in Figure 5. Although the predictions of both models are in good agreement with the experimental data here, the HMSD model provides better results. The reason why the surface energetic heterogeneity here is not as important as that at 10"Cis that the energy distribution effect becomes less significant in the adsorption equilibria as temperature increases (see Figure 1). This is even confirmed with the binary adsorption dynamics of ethane and propane at 60 O C (Figure 6) where the predictions of the HMSD and MSD models are actually superimposed. This is also explained by the fact that the contribution of surface diffusion to the total flux is reduced as temperature increases, because of the lower adsorbed phase concentration at a higher temperature. Finally we study the binary desorption dynamics of 10% ethane and 10% propane in 4.4 mm full length slabs of Ajax activated carbon at 30 "C and 1atm. The experimentaldata (symbols) are shown in Figure 7 together with the correspondingpredictions of HMSD (solid lines) and MSD (dashed lines) models. Although the results of both models are close to each other for ethane uptake rate, the HMSD model provides better predictions for propane uptake rate. In summary, for single-componentsystems, the surface energy distribution is not significant for adsorption dynamics, and it is important for desorption dynamics only when it is so in describing adsorption equilibrium data. However, the surface energetic heterogeneity is vital in the multicomponent dynamics. The uptake rate of the faster-diffusing/less strongly adsorbed species (ethane) is more affected in the adsorption mode, but in the desorption
Time (Seconds)
Figure 6. Effect of energy distributionon the binary adsorption dynamics of ethane and propane onto an Ajax activated carbon of 4.4 mm full length slabs at 60 O C , 1 atm: (a) 5% ethane and 5% propane, (b) 10% ethane and 5% propane, (c) 20% ethane HMSD model, (- - -1 MSD model. and 5% propane; (-)
a 0.6 3
ld
2
0.4
.3
';I 0.2 !L
1,Li-Y - _- - _- _
Q
0.0 0
500
1000 1500 2000 2500
Time (Seconds)
Figure 7. Effect of surface energetic heterogeneityon the binary desorption dynamics of 10% ethane and 10% propane onto 4.4 mm full length slabs of Ajax activated carbon at 30 O C , 1 atm: (-) HMSD model, (- - -) MSD model. mode, the uptake rate of the slower-diffusing/morestrongly adsorbed species (propane) is more affected.
Conclusions A multicomponent sorption dynamics model allowing for the energy distribution for both equilibrium and kinetics rather than for equilibrium only has been successfully developed to study the adsorption of gases in a large activated carbon. By using information of singlecomponent equilibrium and mass transfer, this model is found to be able to accurately predict the multicomponent adsorption dynamics. The agreement between the theory and the experimental data is excellent. Although there is very limited effect on the adsorption dynamics of a single component, the surface energetic heterogeneity plays a significant role in the desorption dynamics of single species and the adsorption kinetics of multicomponent systems.
Hu and Do
2536 Langmuir, Vol. 9, No. 10,1993
When the energy distribution is not important in the isotherm, its effect on the sorption dynamics can also be ignored. The role of surface energetic heterogeneity becomes less important for both equilibrium and dynamics as the temperature increases. For low temperatures, the energy distribution has the maximum effect on the sorption dynamics.
4 0
Acknowledgment. Financial support from the Australian Research Council and the Research Excellence Grants Scheme of the University of Queensland are gratefully acknowledged.
JP
Glossary ratio of the surface activation energy to the heat of adsorption Biot number (defined in Table I) isotherm parameter (mVkmo1) isotherm parameter (ms/kmol) adsorbate concentration in the macropore (kmol/ m3) adsorbate concentration in the bulk (kmol/m3) initial adsorbate concentration in the macropore (km01/m3) characteristic concentration for the fluid concentration (kmol/m3) adsorbed concentration in the particle (kmol/m3) characteristic concentration for the adsorbed concentration (kmol/mS) observed adsorbed concentration in the particle (kmo~m3) isotherm parameter (kmoVm3) macropore diffusivity (m2/s) surface diffusivity (m2/s)
E e F
f H HMSD J,
km MSD NC r
R S
T t X
YP
yb
y,
surface diffusivity at infinite temperature (m2/s) adsorbate-adsorbent interaction energy (kJ/mol) nondimensional energy (defined in Table I) energy distribution function nondimensional energy distribution function (defined in Table I) function defined in Table I heterogeneous macropore and surface diffusion flux through the macropore (kmol/(m2 8)) flux through the solid (kmol/(m2 8)) film mass transfer coefficient (m/s) macropore and surface diffusion number of component particle radial position (m) particle radius (m) or gas constant (kJ/(kmol K)) geometric factor (=O, 1, 2 for slab, cylinder, and sphere, respectively) temperature (K) time (8) nondimensional particle radial position nondimensional adsorbate concentration in the macropore nondimensional adsorbate concentration in the bulk nondimensional adsorbed concentration in the particle
Greek symbols 6 model parameter defined in Table I BM particle macropore porosity x model parameter defined in Table I a model parameter defined in Table I model parameter defined in Table I u* model parameter defined in Table I rl 7 nondimensional time defined in Table I
