Adsorption of Butane Isomers and SF6 on Kureha Activated Carbon: 2

Characterization of Catalysts under Working Conditions with an Oscillating Microbalance Reactor. D. Chen , E. Bjorgum , K.O. Christensen , A. Holmen ,...
0 downloads 0 Views 102KB Size
Download PDF
1704

Langmuir 2004, 20, 1704-1710

Adsorption of Butane Isomers and SF6 on Kureha Activated Carbon: 2. Kinetics Weidong Zhu,*,† Freek Kapteijn,† Johan C. Groen,‡ Marco J. G. Linders,† and Jacob A. Moulijn† Reactor & Catalysis Engineering, Applied Catalyst Characterization, DelftChemTech, Delft University of Technology, Julianalaan 136, 2628 BL, Delft, The Netherlands Received June 25, 2003. In Final Form: October 3, 2003 The desorption kinetics of n-butane and isobutane in Kureha carbon has been investigated by means of the TEOM technique. The model used to describe the desorption profiles is based on the nonlinear To´th type adsorption isotherm and the overall rate of desorption controlled by both mass transfer across the gas film surrounding each particle and micropore diffusion. The strong concentration-dependent micropore diffusion in Kureha carbon could be well described by the structural approach proposed by Do (Chem. Eng. Sci. 1996, 51, 4145-4158), in which the diffusivity at zero coverage appeared to be independent of loading. The concentration dependence of micropore diffusivities in the structural approach is stronger than the so-called Darken correction; for n-butane it is stronger than that for isobutane. Under similar conditions, the diffusivities of n-butane in Kureha carbon are slightly larger than those of isobutane. The diffusivity activation energy at zero loading for n-butane is larger than that for isobutane because of the penetration of n-butane molecules in the smaller micropores of Kureha carbon, in which there are stronger interactions between adsorptive and adsorbent.

Introduction Diffusion of gases in carbon molecular sieve (CMS) adsorbents has been intensively investigated with various techniques such as pulse chromatographic,1-3 gravimetric uptake,3-8 batch column adsorption,8-10 volumetric,3,11,12 gas permeation,10 and isotope exchange13 methods. Reid et al.6 investigated the diffusion of oxygen, nitrogen, argon, and krypton in the commercial CMS supplied by Air Products and Chemicals Inc. and pointed out that the adsorption kinetics obeyed a linear driving force (LDF) mass transfer model for the experimental conditions studied, which is not unexpected for CMS since often they are produced by pore mouth plugging. The LDF model was also successfully used to describe the adsorption kinetics of nitrogen in Takeda CMS-5A.1 In such an approach, the micropore diffusivity is often assumed to be independent of loading. This is generally true for * To whom correspondence should be addressed. Fax: +31-152785006. E-mail: [email protected]. † Reactor & Catalysis Engineering. ‡ Applied Catalyst Characterization. (1) Kawazoe, K.; Suzuki, M.; Chihara, K. J. Chem. Eng. Jpn. 1974, 7, 151-157. (2) Chihara, K.; Suzuki, M.; Kawazoe, K AIChE J. 1978, 24, 237246. (3) Loughlin, K. F.; Hassan, M. M.; Fatehi, A. I.; Zahur, M. Gas Sep. Purif. 1993, 7, 264-273. (4) Ruthven, D. M.; Raghaven, N. S.; Hassan, M. M. Chem. Eng. Sci. 1986, 41, 1325-1332. (5) Ruthven, D. M. Chem. Eng. Sci. 1992, 47, 4305-4308. (6) Reid, C. R.; O′koye, I. P.; Thomas, K. M. Langmuir 1998, 14, 2415-2425. (7) Chen, Y. D.; Yang, R. T.; Uawithya, P. AIChE J. 1994, 40, 577585. (8) LaCava, A. I.; Koss, V. A.; Wickens, D. Gas Sep. Purif. 1989, 3, 180-186. (9) Nguyen, C.; Do, D. D. Langmuir 2000, 16, 1868-1873. (10) Rutherford, S. W.; Do, D. D. Carbon 2000, 38, 1339-1350. (11) Srinivasan, R.; Auvil, S. R.; Schork, J. M. Chem. Eng. J. 1995, 57, 137-144. (12) Huang, Q. L.; Sundaram, S. M.; Farooq, S. Langmuir 2003, 19, 393-405. (13) Rynders, R. M.; Rao, M. B.; Sircar, S. AIChE J. 1997, 43, 24562470.

diffusion in microporous materials in the linear adsorption range.14,15 The concentration-dependent diffusion of CO2 in Takeda CMS-5A was investigated by Rutherford and Do,10 who reported that the concentration dependence of the micropore diffusivity could be well correlated with the Darken equation. Recently, Huang et al.12 revisited the concentration-dependent diffusion of oxygen and nitrogen in three CMS adsorbents and concluded that the extracted micropore transport parameters had a much stronger dependence on loading than that expected from Darken’s equation. In summary, the overall transport rate in CMS adsorbents is generally controlled by diffusion inside the micropores and the corresponding diffusivities are concentration dependent, as would be inferred from the generally heterogeneous nature of the adsorptiveadsorbent interactions. The diffusion in activated carbons having a wide pore size distribution, covering from micropores to macropores, is far more complicated than that in CMS adsorbents. Do and co-workers16-25 and other investigators26-28 have studied transport phenomena of probe molecules in commercial samples of activated carbon such as Norit and Ajax. Wang et al.16 examined five different kinetic models, (14) Do, D. D. Adsorption Analysis: Equilibrium and Kinetics; Imperial College Press: London, 1998. (15) Ka¨rger, J.; Ruthven, D. M. Diffusion in Zeolites and Other Microporous Solids; John Wiley & Sons: New York, 1992. (16) Wang, K.; Qiao, S.; Hu, X.; Do, D. D. Adsorption 2001, 7, 51-63. (17) Hu, X.; Rao, G. N.; Do, D. D. Gas Sep. Purif. 1993, 7, 197-206. (18) Hu, X.; Do, D. D. Langmuir 1993, 9, 2530-2536. (19) Mayfield, P. L. J.; Do, D. D. Ind. Eng. Chem. Res. 1991, 30, 1262-1270. (20) Prasetyo, I.; Do, D. D. AIChE J. 1999, 45, 1892-1900. (21) Do, D. D.; Wang, K. AIChE J. 1998, 44, 68-82. (22) Do, D. D.; Do, H. D. Adsorption 2001, 7, 189-209. (23) Prasetyo, I.; Do, D. D. Chem. Eng. Sci. 1998, 53, 3459-3467. (24) Do, D. D.; Do, H. D.; Prasetyo, I. Chem. Eng. Sci. 2000, 55, 1717-1727. (25) Do, D. D.; Wang, K. Carbon 1998, 36, 1539-1554. (26) Liu, X.; Pinto, N. G. Carbon 1997, 35, 1387-1397. (27) Scholl, S.; Kajszika, H.; Mersmann, A. Gas Sep. Purif. 1993, 7, 207-212. (28) Linders, M. J. G.; van den Broeke, L. J. P.; Nijhuis, T. A.; Kapteijn, F.; Moulijn, J. A. Carbon 2001, 39, 2113-2130.

10.1021/la030258d CCC: $27.50 © 2004 American Chemical Society Published on Web 02/06/2004

Adsorption of Butane Isomers

Langmuir, Vol. 20, No. 5, 2004 1705

which are (a) dual pore and surface diffusion, (b) macropore, surface, and micropore diffusion, (c) macropore, surface, and finite mass exchange, (d) finite mass exchange, and (e) macropore and micropore diffusion, for the diffusion of ethane and propane and their mixtures in two activated carbon samples (Norit and Ajax). These authors concluded that the energetic heterogeneity of the system for both adsorption and diffusion should be taken into account and the role of the surface (micropore) diffusion in the overall kinetics was significant. In terms of the concentration dependence, the authors figured out that the surface diffusion exhibited a much stronger dependence on the adsorbed phase concentration than the Darken relation. Do29 proposed a model for activated carbon that addressed the effect of structure on the transport surface diffusivity. For the To´th isotherm, the dependence of diffusivity D on fractional loading takes the form

D)

D0 (1 - θm)(1/m)+1

) D0Γ

(1)

with

Γ)

1 m (1/m)+1

(1 - θ )

where D0 is the diffusivity at zero loading, m is the parameter in the To´th model, θ corresponds to the fractional loading, and Γ is conventionally the so-called thermodynamic correction factor. Compared to the Darken relation for the To´th isotherm

D)

D0 1 - θm

) D0Γ

(2)

with

Γ)

1 1 - θm

eq 1 shows a much stronger dependence on loading. Indeed the extracted apparent diffusivities of ethane in Ajax activated carbon follow eq 1, the so-called structural approach.29 Kureha carbon is a pure micropore material,30 which is interesting to study. Up to now, only Linders et al.28 have investigated the diffusion of n-butane in Kureha carbon at very low pressures by means of the TAP-like technique, the so-called Multitrack. In our previous work,30 the equilibrium adsorption of the butane isomers in Kureha carbon was studied by both volumetric and TEOM techniques. The measurements by these two techniques show excellent agreement. The TEOM technique has been successfully applied to determine micropore diffusivities in zeolites.31-34 Unlike conventional gravimetric and volumetric methods, the TEOM technique minimizes external mass and heat transfer limitations in transient experiments due to a high flow rate of the carrier gas (29) Do, D. D. Chem. Eng. Sci. 1996, 51, 4145-4158. (30) Zhu, W.; Groen, J. C.; Kapteijn, F.; Moulijn, J. A. Submitted to Langmuir. (31) Zhu, W.; Kapteijn, F.; Moulijn, J. A. Microporous Mesoporous Mater. 2001, 47, 157-171. (32) Giaya, A.; Thompson, R. W. Microporous Mesoporous Mater. 2002, 55, 265-274. (33) van Donk, S.; Broersma, A.; Gijzeman, O. L. J.; van Bokhoven, J. A.; Bitter, J. H.; de Jong, K. P. J. Catal. 2001, 204, 272-280. (34) Rebo, H. P.; Chen, D.; Brownrigg, M. S. A.; Moljord, K.; Holmen, A. Collect. Czech. Chem. Commun. 1997, 62, 1832-1842.

through the sample bed without affecting measurements. One of the objectives in the present study is to use the TEOM technique to investigate and describe the adsorption kinetics of the butane isomers in Kureha carbon. This essentially microporous carbon allows the direct study of the surface diffusion. In addition, the effects of the external mass and heat transfer limitations on relatively fast transient processes will be evaluated. In part 1 the analysis of equilibrium adsorption in Kureha carbon has shown that the adsorption properties change with molecular shape and size of the probes.30 In the present study, Kureha carbon is further characterized in terms of adsorption kinetics of the butane isomers. Mathematical Model Desorption of a single component, adsorbed in microporous particles of spherical shape and uniform size, into a pure purge gas under the isothermal condition is considered. The adsorptive concentration in the solid is initially assumed to be uniform and in equilibrium with the adsorptive in the gaseous phase. In addition, the following assumptions are made: (1) Diffusion in the microporous carbon is described by Fick’s law with a concentration-dependent diffusivity. (2) The overall desorption process is controlled by both micropore diffusion and external mass transfer across the gas film surrounding each particle. (3) The sample bed is taken as a well-mixed reservoir, thus ignoring concentration variations in the spatial directions. (4) An ideal gas behavior of the adsorptive in the void space and constant total flow through the sample bed are assumed. The mass balance of the adsorptive in the void space is expressed by the equation

bVb

( )

dCb 3 ) -ΦvCb + (1 - b)Vb [k (C - Cb)] dt Rp f s

(3)

where Rp is the radius of a particle, Vb is the volume of the sample bed, b is the void fraction of the bed, Φv is the total flow rate through the sample bed, kf is the external mass transfer coefficient, Cb is the concentration in the fluid phase, and Cs is the concentration in the fluid phase at the surface of a particle. The mass balance equation describing the concentration distribution of the adsorbed species in a spherical particle takes the form

(

) (

)

∂2q 2Γ ∂q ∂Γ ∂q ∂q ∂q 1 ∂ 2 ) 2 + +Γ 2 r D0Γ ) D0 ∂t r ∂r ∂r r ∂r ∂r ∂r ∂r

(4)

where q is the concentration in the solid phase, r is the radial coordinate of a particle, D0 is the micropore diffusivity at zero coverage, and Γ is the thermodynamic factor, which may be expressed by either eq 1 or eq 2 for the To´th isotherm. The associated boundary conditions are

( ∂q∂r)|

-D0 Γ

r)Rp

) kf(Cs - Cb);

|

∂q )0 ∂r r)0

(5)

In eqs 3 and 5, Cs is correlated with the adsorbed concentration at the surface of a particle via the isotherm

1706

Langmuir, Vol. 20, No. 5, 2004

Zhu et al.

model chosen to represent the measured equilibrium data. For the To´th isotherm

q|r)Rp ) qsat

Kps m 1 m

[1 + (Kps) ] /

) qsat

K′Cs

(6)

[1 + (K′Cs)m]1/m

where qsat is the saturation limit, K or K′ is the affinity parameter or equilibrium constant, and ps represents the corresponding pressure in the fluid phase at the surface of a particle. The initial conditions for the desorption are

Cs ) Cb ) C0; q ) q0 ) qsat

K′C0

(7)

[1 + (K′C0)m]1/m

For convenience the following dimensionless variables are defined

X)

r C q ; Y) ; Q) Rp C0 q0

(8)

The balance equation, eq 3, becomes

( )|

D0 Y dY ∂Q )- -β 2 Γ dt τb ∂X R p

(9)

x)1

and the parameters

τb )

bVb (1 - b) q0 ; β)3 Φv b C0

(10)

The balance equation over a particle can be expressed by

(

)

D0 2Γ ∂Q ∂Γ ∂Q ∂2Q ∂Q ) 2 + +Γ 2 ∂t X ∂X ∂X ∂X R ∂X p

(11)

The dimensionless boundary conditions are

|

∂Q ∂X

{

Rpkf C0 Q|X)1 ) Ysat m X)1 D0Γ|X)1 q0 K′[(q ) - (q Q| 0

|

∂Q ∂X

X)1)

X)0

}

m 1 m

]/

;

) 0 (12)

and the initial conditions for the desorption are

Y|t)0 ) 1; Q|t)0 ) 1

(13)

Using the method of lines,35 the set of partial differential equations was discretized by a finite difference scheme to obtain a set of ordinary differential equations (ODEs), which are then solved simultaneously with the Livermore ODE solver for sparse systems (LSODES).36 The radius of an adsorbent particle was discretized in 51 grid points. A three-point centered approximation was used for the calculations of the spatial derivatives. In the model fitting the determination of the only unknown parameter, i.e., the diffusivity at zero coverage, D0, is based on the nonlinear least-squares method, minimizing the sum of the squared residuals (SSRs) between the model predictions (Qcal) and the experimental data (Qobs). Starting with an initial guess of D0, the minimization of the SSR is achieved by varying the (35) Schiesser, W. E. The Numerical Method of Lines: Integration of Partial Differential Equations; Academic Press: San Diego, 1991. (36) Hindmarsh, A. C. In Scientific Computing; Stepleman, R. S., Carver, M., Eds.; Elsevier: Amsterdam, 1983.

parameter according to the Simplex or the LevenbergMarquardt method until a minimum is encountered and convergence criteria have been reached. Experimental Section Adsorbent and Adsorptives. The adsorbent Kureha carbon and the adsorptives used for transient experiments were the same as those for equilibrium measurements.30 The sieved spherical Kureha carbon had an average particle radius of 1.7 × 10-4 m, as determined by scanning electron microscopy. The detailed textural properties of the adsorbent can be found in the previous paper.30 Apparatus. A Rupprecht & Patashnick TEOM 1500 mass analyzer (100 mg sample volume) was used for measurements of transient adsorption and desorption in Kureha carbon. A detailed description of the TEOM operating principles is given elsewhere.37 Procedure. The usual pattern followed in these experiments was to regenerate a given adsorbent sample and then carry out an adsorption-desorption cycle, with continuous monitoring of the mass changes. The oscillating microbalance was connected through a data acquisition board to a personal computer, with data acquisition software LabView. The sample bed was loaded with a thin layer of the Kureha carbon particles, whose weight was 13. 5 mg. An adsorption run was initiated by replacing the helium stream by a predetermined mixture of helium and the sample gas. The feed was maintained until the sample was equilibrated as indicated by constant mass change. Desorption was then carried out by changing the heliumfeed gas mixture to pure helium and running until the sample mass change returned to its initial value. Nearly constant total flows were maintained during the uptake and desorption experiments. This essentially minimized the experimental errors that could be caused by a system pressure change. In the present study, the total flow rate through the sample bed was 200 cm3 (NTP) min-1 (NTP: 298 K and 101.325 kPa). The TEOM 1500 analyzer can store current data in up to three data files with different time intervals simultaneously. For fast adsorption and desorption processes, a data file with a storage interval of 0.84 s was used, while the file with an interval of either 10 or 60 s was used for slow processes. The detailed experimental procedures for transient measurements are given elsewhere.31

Results and Discussion Adsorption versus Desorption. In the nonlinear adsorption range, assuming the isotherm is convex and when the concentration-dependent micropore diffusivity follows the strongly nonlinear behavior, adsorption and desorption processes exhibit strong asymmetry.14 During the uptake process the diffusivity increases with time on stream, i.e., with loading. Conversely, during the desorption process the diffusivity decreases as time progresses and, therefore, proceeds considerably more slowly than the uptake process. A comparison of adsorption and desorption curves is shown in Figure 1 for n-butane in Kureha carbon at 353 K. Two factors are important for extracting transport parameters from uptake and desorption curves. Experimentally, for a faster transient process, it demands a higher time-resolution device to follow the mass change in the adsorbed phase or the concentration change in the gas phase. In this point of view, the desorption process is easier to follow than the uptake. Second, temperature changes inside adsorbent particles during the transient process may occur, which are proportional to the adsorption or desorption rate. So, in the nonlinear adsorption range the heat effects upon adsorption are more pronounced than those upon desorption. The isothermal conditions are then easier maintained for the desorption mode.31 From these considerations it appears that the (37) Zhu, W.; van de Graaf, J. M.; van den Broeke, L. J. P.; Kapteijn, F.; Moulijn, J. A. Ind. Eng. Chem. Res. 1998, 37, 1934-1942.

Adsorption of Butane Isomers

Figure 1. Adsorption and desorption cycle of n-butane in Kureha carbon at 353 K. Adsorption at an inlet adsorptive concentration of 0.264 mol m-3, corresponding with the equilibrium amount adsorbed of 1280 mol m-3, and desorption in flowing He with a rate of 200 cm3 (NTP) min-1.

Langmuir, Vol. 20, No. 5, 2004 1707

Figure 3. Normalized desorption profiles of isobutane in Kureha carbon at 338 K and different initial loadings. Lines are the model fits. (4) q0 ) 1210 mol m-3; (O) q0 ) 1900 mol m-3; (3) q0 ) 2510 mol m-3. Table 1. Key Operating Parameters for the TEOM Studies microbalance diameter of packed bed sample bed mean particle radius bed porosity volume particle density fluid He purge flow rate

d ) 4.0 × 10-3 m Rp ) 1.7 × 10-4 m b ) 0.4 Vb ) 2.05 × 10-8 m3 F ) 1098 kg m-3 Φv ) 200 cm (NTP) min-1

Table 2. Adsorption Parameters Used as Inputs in the Modelinga qsat/mol m-3

K′/m3 mol-1

KH

m

298 338 353 373 393

6.80 × 103 7.08 × 103 6.96 × 103 7.20 × 103 7.36 × 103

n-Butane 140 20.4 8.88 4.15 1.88

9.52 × 105 1.44 × 105 6.18 × 104 2.99 × 104 1.38 × 104

0.333 0.320 0.332 0.328 0.332

298 338 353 373 393

6.35 × 103 6.32 × 103 6.32 × 103 6.32 × 103 6.40 × 103

Isobutane 59.0 11.2 6.08 2.83 1.26

3.74 × 105 7.11 × 104 3.84 × 104 1.79 × 104 8.05 × 103

0.362 0.350 0.349 0.354 0.359

T/K

Figure 2. Normalized desorption profiles of n-butane in Kureha carbon. Lines are the model fits. (4) 298 K, q0 ) 3200 mol m-3; (O) 338 K, q0 ) 1710 mol m-3; (3) 353 K, q0 ) 1280 mol m-3.

transport parameters are extracted under better controlled conditions from desorption curves, although the concentration dependence is more sensitive to the uptake than to the desorption mode.14 In this study all micropore diffusivities will be derived from the measured desorption curves. Thermodynamic Factor. The desorption curves of the butane isomers in Kureha carbon were measured at multiple temperatures and different initial loadings. Figure 2 shows some desorption curves of n-butane at temperatures from 298 to 353 K, and Figure 3 represents desorption curves of isobutane at 338 K and different initial loadings. The input parameters for the fits are listed in Tables 1-3. The values of D0 estimated by using the model equations (9 and 11) in combination with either eq 1 or eq 2 from the desorption curves are presented in Table 4, together with the experimental conditions such as the initial concentration C0 and the corresponding loading q0. In general, both models capture the desorption curves very well. One of the generally used models for describing surface and micropore diffusion is based on the gradient of chemical potential as driving force for the diffusion. This leads to a relation in which the Fickian diffusivity can be represented by a diffusivity at zero coverage, D0, the socalled corrected diffusivity, times a thermodynamic cor(38) Wakao, N.; Funazkri, T. Chem. Eng. Sci. 1978, 33, 1375-1384. (39) Weast, R. C.; Astle, M. J. Handbook of Chemistry and Physics; CRC Press: Boca Raton,FL, 1990.

a Data from ref 30, units mol kg-1 and kPa-1 changed into mol m-3 and m3 mol-1 by multiplying by the particle density (1098 kg m-3) and 10-3RgT (Rg is the universal gas constant, 8.314 J mol-1 K-1), respectively.

Table 3. Values of Mass and Heat Transfer Parameters Across the Gas-film Surrounding Adsorbent Particles and of the Mean Heat Capacity Per Unit Particle Volume of Kureha Carbon kf a/m s-1 T/K

n-butane

isobutane

10-3ha/ J m-2 s-1 K-1

10-6FCpb/ J m-3 K-1

298 338 353 373 393

0.353 0.429 0.458 0.499 0.540

0.355 0.430 0.460 0.500 0.542

1.23 1.32 1.35 1.39 1.43

0.781 0.999 1.06 1.14 1.20

a Calculated from the correlation proposed by Wakao and Funazkri.38 b Data of carbon heat capacity from ref 39 and density of Kureha carbon particles of 1098 kg m-3.

rection factor Γ, the Darken correction. Usually, D0 is assumed to be concentration independent. According to our results in this model, the estimated diffusivity D0 is, however, strongly dependent on the adsorbed concentration and its value significantly increases with initial loading, as shown in Table 4. This was also observed by

1708

Langmuir, Vol. 20, No. 5, 2004

Zhu et al.

Table 4. Experimental Conditions, Estimated Diffusivities, and Values of the Biot Number Defined by Equation 15 109D0/m2 s-1 adsorptive n-butane

T/K 298 338 353 373 393

isobutane

298 338 353 373 393

C0/mol

m-3

0.308 0.275 0.819 1.34 0.264 0.788 1.29 0.155 0.512 1.25 0.148 0.490 1.20 0.317 0.178 0.569 1.39 0.173 0.551 1.35 0.165 0.528 1.29 0.159 0.508 1.24

103q

0/mol

3.20 1.71 2.44 2.79 1.28 1.96 2.30 0.693 1.24 1.78 0.450 0.875 1.33 2.79 1.21 1.90 2.51 0.888 1.49 2.06 0.595 1.08 1.59 0.370 0.735 1.15

m-3

Darkena

structuralb

Bi

1.52 ( 3.15 ( 0.02 4.39 ( 0.01 4.86 ( 0.00 3.87 ( 0.18 5.23 ( 0.01 5.84 ( 0.03 5.92 ( 0.02 7.49 ( 0.02 9.05 ( 0.01 8.41 ( 0.07 10.0 ( 0.1 11.6 ( 0.1 1.05 ( 0.00 1.86 ( 0.16 2.40 ( 0.01 3.09 ( 0.02 2.74 ( 0.06 3.50 ( 0.00 4.25 ( 0.00 3.50 ( 0.02 4.22 ( 0.02 5.06 ( 0.01 4.83 ( 0.28 5.64 ( 0.04 6.30 ( 0.10

0.0564 ( 0.0001c 0.214 ( 0.002 0.221 ( 0.001 0.220 ( 0.000 0.306 ( 0.016 0.338 ( 0.003 0.350 ( 0.003 0.572 ( 0.001 0.569 ( 0.001 0.569 ( 0.001 0.907 ( 0.008 0.910 ( 0.005 0.907 ( 0.005 0.0503 ( 0.0004 0.171 ( 0.006 0.164 ( 0.004 0.164 ( 0.001 0.251 ( 0.002 0.252 ( 0.001 0.251 ( 0.000 0.399 ( 0.000 0.393 ( 0.001 0.402 ( 0.000 0.607 ( 0.007 0.607 ( 0.002 0.616 ( 0.008

1.12d 2.36 2.29 2.31 4.11 3.73 3.60 4.96 4.98 4.98 7.33 7.31 7.33 3.21 6.03 6.29 6.25 8.13 8.09 8.13 11.9 12.1 11.8 18.9 18.9 18.6

0.02c

a Model with the Darken relation, i.e., eq 2. b Model with the structural approach, i.e., eq 1. c 95% confidence limit. extracted from the model with the structural approach.

Figure 4. Thermodynamic correction factor as a function of coverage at 373 K for n-butane (solid line) and isobutane (dashed line). (a) structural approach eq 1; (b) Darken relation eq 2.

Do22,29 who found that the surface diffusion in activated carbon had a much stronger dependence on the concentration than the Darken relation. Recently, the same observation was reported by Huang et al.12 for the diffusion of oxygen and nitrogen in the CMS samples. This means that the thermodynamic correction factor according to the Darken relation is not sufficient to account for the increase. Apparently, the Darken relation fails also to capture the concentration-dependent diffusion in Kureha carbon. On the other hand, in the model with the concentration dependence described by the structural approach,29 i.e., eq 1, the extracted values of the fitting parameter D0 at the same temperature are independent of initial loading (Table 4). The model appropriately describes the desorption curves. The fitted model lines are shown in Figures 2 and 3. The dependence of the apparent or Fickian diffusivity D on loading predicted by the structural approach model is far stronger than that exhibited by the Darken relation. Figure 4 gives a comparison of the loading dependencies of Γ based on the structural approach and the Darken relation. From Figure 4, it is also seen that the loading dependence of Γ for n-butane is somewhat stronger than that for isobutane.

d

Using diffusivities

The structural approach model addresses the effect of carbon structure on diffusion. The diffusion mechanism in activated carbon is considered as the penetration of adsorptive molecules into graphitic layer units, diffusion through it and evaporation out of it. Upon leaving the graphitic units, the molecules then rejoin with other molecules diffusing through the porous medium via the larger void space parallel to the graphitic layers. They in turn then diffuse through the amorphous region of activated carbon. The sequence of these steps repeats itself in a periodic pattern.29 If the transport of adsorptive molecules through the graphitic layers is very fast, the overall flow of diffusing species will be controlled by the transport through the void space in parallel to the graphitic region and through the disordered regions joining the two consecutive graphitic units. In this case, the concentrationdependent diffusivity is proportional to the inverse of the slope of the adsorption isotherm at gas-phase concentration C, i.e., (dq/dC)-1, which is similar to that proposed by Ka¨rger.40 In principle this implies a diffusion model based on gas-phase concentration gradient as driving force with constant diffusivity. Because the structural approach model well describes the desorption curves over different initial loadings, in the further analysis the diffusivities extracted from the structural model will be used. The functional dependence of D0 on temperature seems to follow the Arrhenius law

( )

D0 ) D0∞ exp -

Ea RgT

(14)

where D0∞ is the pre-exponential factor and Ea is the diffusivity activation energy. Plotting D0 versus the inverse of the absolute temperature, a straight line is observed, as indicated in Figure 5. The parameter values are summarized in Table 5. The reported literature data for n-butane in Kureha carbon are also included in Figure 5 and Table 5. The current results are in good agreement with those from Linders et al.28 who used the TAP (40) Ka¨rger, J. Langmuir 1988, 4, 1289-1292.

Adsorption of Butane Isomers

Langmuir, Vol. 20, No. 5, 2004 1709

Figure 5. Corrected diffusivity D0 as a function of 1/T for the butane isomers in Kureha carbon. (2) n-butane; (b) isobutane; (4) n-butane, from Linders et al.28 Table 5. Values of the Arrhenius Diffusivity Parameters and the Isosteric Heat of Adsorption at Zero Coverage for the Butane Isomers in Kureha Carbon adsorptive

D0∞/m2 s-1

Ea/ kJ mol-1

n-butane

3.00 × 10-6 6.04 × 10-6 1.59 × 10-6

27.9 28.8 25.7

isobutane a

Q0st/ kJ mol-1

technique

ref

45.2 46.3 41.8

TAP TEOM TEOM

28 a a

This study.

technique to measure the diffusivities of n-butane at very low loadings. Although the diffusivities of n-butane are slightly larger than those of isobutane under similar conditions, the derived diffusivity activation energy for n-butane is also somewhat higher than that for isobutane. This observation is significantly different from the diffusion of linear and branched alkane isomers in molecular sieves, for example, in silicalite-1. The diffusivity of normal hexane is higher by 1 order of magnitude than that of 3-methylpentane, and the derived diffusivity activation energy for the linear isomer is much lower than that for the branched one.31 In addition, the concentration dependence of diffusivity is well described by the Darken relation. These discrepancies could be attributed to a different pore size distribution. In general, molecular sieves have well-defined pore sizes, resulting in the system homogeneity for adsorption and diffusion and leading to large differences in the transport between linear and branched alkanes. Due to its wider pore size distribution, Kureha carbon does not discriminate that strongly between the butane isomers. The magnitude of Ea reflects the energy barrier during diffusion, which is related to the interactions between diffusing species and adsorbent. The isosteric heat at zero coverage for n-butane is higher than that for isobutane. This is also the case for the derived diffusivity activation energy at zero coverage (Table 5). The penetration of n-butane molecules into smaller micropores, in which there are stronger interactions between n-butane and adsorbent, results in a stronger temperature dependence for diffusion. External Mass Transfer. The effects of the external mass transfer on the overall adsorption or desorption process can be evaluated in terms of the Biot number.14 In the linear adsorption range, the Biot number is defined by the equation

Bi ) Rpkf/KHD0

(15)

where Bi is the Biot number and KH is the Henry law constant in dimensionless form and its values are shown in Table 2. Only in the case of Bi . 1, the overall rate is

Figure 6. Simulated temperature change of the carbon particle during the first 50 s desorption of n-butane under similar initial partial pressures at different temperatures. (a) 298 K, C0 ) 0.308 mol m-3; (b) 338 K, C0 ) 0.275 mol m-3; (c) 353 K, C0 ) 0.264 mol m-3.

controlled by micropore diffusion. The values of Bi calculated from eq 15, which are included in Table 4, are not far away from unity. In addition, in the nonlinear adsorption range, the values of the Biot number are smaller than those presented in Table 4 due to the contribution from Γ. It means that the external mass transfer plays an important role in the overall desorption rate, especially in the initial stage, in which the apparent diffusion rate in the solid is higher. So in the current case the mass transfer across the gas film has to be taken into account in order to extract micropore diffusivities. Heat Effects. Heat is released upon adsorption and absorbed upon desorption. The temperature change in the adsorbent particles depends on the interplay between the rate of heat and mass transfer with the surrounding. By assuming the temperature within the particles uniform and all the heat transfer resistance in the gas film surrounding each particle, a lumped thermal model is used to evaluate the heat effects14

FCp

( )( )|

3q0D0 dT ∂Q ) (-∆Had) Γ dt ∂X Rp2

X)1

-

3 h(T - Tb) Rp (16)

where ∆Had is the adsorption enthalpy, FCp is the mean heat capacity per unit particle volume, T is the temperature in the particles, Tb is the surrounding temperature, which is assumed constant, and h is the heat transfer coefficient. For simplification, -∆Had and Q0st are assumed to be identical by neglecting any temperature and loading dependence. The values of Q0st are included in Table 5. The input values of h and FCp are listed in Table 2. Figure 6 shows the temperature change (∆T ) T - Tb) of Kureha carbon particle during the first 50 s of desorption of n-butane under similar initial partial pressures at different temperatures. The desorption rate increases with increasing initial loading and diffusivity. At a similar initial concentration in the gas phase, the initial loading in the solid decreases with an increase in temperature (Table 4). Even though the diffusivity increases with temperature, the maximal temperature difference decreases with increasing temperature at the same initial concentration in the gas phase, as indicated in Figure 6. It is generally true for the case that the activation energy for diffusion is lower than the heat of adsorption. The temperature change inside the adsorbent particle is more pronounced when the initial loading is increased, as Figure 7 demonstrates for isobutane at 338 K.

1710

Langmuir, Vol. 20, No. 5, 2004

Zhu et al.

pendent micropore diffusion. Although the kinetic diameter of n-butane is smaller than that of isobutane and its diffusivity D0 somewhat larger, its diffusivity activation energy at zero coverage is higher than that for isobutane. The linear n-butane molecule enables penetration into smaller micropores, resulting in stronger interactions between adsorbent and adsorptive, as reflected by the isosteric heat of adsorption at zero coverage. This also leads to a stronger temperature dependence for n-butane diffusion in Kureha carbon. Glossary Bi C0 Figure 7. Simulated temperature change of the carbon particle during the first 50 s desorption of isobutane at 338 K and different initial loadings. (a) q0 ) 1210 mol m-3; (b) q0 ) 1900 mol m-3; (c) q0 ) 2510 mol m-3.

The simulation shows that the temperature change for all cases is well below 1 K. So the heat effects can be considered to be absent during the desorption of the butane isomers in Kureha carbon under the investigated conditions. The above analysis indicates that the heat effects on the desorption are negligible, while the mass transfer resistance across the gas film is present in all cases. The diffusivity D0 extracted by the model with the Darken relation shows a strong dependence on loading. This is, in general, true for diffusion in activated carbon having a wide pore size distribution. Instead the structural approach enables description of the desorption curves very well and the estimated diffusivity at zero coverage is concentration independent. The derived values of the Arrhenius parameters for n-butane are almost the same as those determined by the low-pressure TAP technique,28 with which the diffusivities were measured at very low loadings. This further confirms the current approach. To examine the structural model, Do29 used eq 1 to correlate the extracted surface diffusivities of ethane in Ajax activated carbon. Because the macropore and surface diffusion was in parallel for ethane in Ajax activated carbon, the concentration-dependent surface diffusivity could be only extracted by assuming constant diffusivity for the macropore diffusion. Additionally, the structural model was examined using few data points of the extracted surface diffusivity in a narrow temperature range from 303 to 333 K. In the present study, the adsorbent used is a pure microporous material, a simple model enables description of the desorption curves over the whole time series very well, and no correction is needed to extract the micropore diffusivities. In addition, the structural model has been examined in a wider temperature rang from 298 to 393 K. Thus the current approach enhances the validity and credibility of the structural model to describe stronger concentration-dependent diffusion in activated carbons. Conclusions Kureha carbon has been further characterized in terms of desorption kinetics using the butane isomers as probes. Both micropore diffusion and mass transfer across the gas film around the particles control the overall transport kinetics. Heat effects can be neglected under the investigated conditions. The conventional Darken relation fails to capture the concentration-dependent diffusion in Kureha carbon. Alternatively, the structural model proposed by Do (Chem. Eng. Sci. 1996, 51, 4145-4158) appropriately describes this stronger concentration-de-

Cb Cs d D D0 D0∞ Ea h K K′ kf KH ps p q q0 qsat Q Q0st r Rp Rg t T Tb Vb X Y

Biot number defined by eq 15 initial concentration in the gas phase for desorption, mol m-3 bulk concentration in the gas phase, mol m-3 concentration in the gas phase at the surface of particles, mol m-3 diameter of TEOM packed bed, m diffusivity, m2 s-1 diffusivity at zero coverage, m2 s-1 pre-exponent factor of the Arrhenius law defined by eq 14, m2 s-1 diffusivity activation energy, kJ mol-1 heat transfer coefficient, J m-2 K-1 equilibrium constant, kPa1equilibrium constant in dimensionless form external mass transfer coefficient, m s-1 Henry law constant in dimensionless form pressure at the surface of particles, kPa pressure, kPa amount adsorbed, mol kg-1 or mol m-3 initial amount adsorbed, mol kg-1 or mol m-3 saturation amount adsorbed, mol kg-1 or mol m-3 dimensionless loading in the solid defined by eq 8 isosteric heat at zero coverage, kJ mol-1 radial coordinate, m radius of Kureha carbon particle, m universal gas constant, 8.314 J mol-1 K-1 time, s temperature, K temperature in the fluid phase, K sample bed volume, m3 dimensionless radial coordinate defined by eq 8 dimensionless concentration in the fluid phase defined by eq 8

Greek letters β b θ F FCp τb ∆Had ∆m ∆T Φv Γ

parameter defined by eq 10 sample bed porosity fractional loading particle density, kg m-3 mean heat capacity per unit particle volume, J m-3 K-1 parameter defined by eq 10 molar enthalpy of adsorption, kJ mol-1 mass change measured with the TEOM, mg temperature difference between particle and fluid phase, K He purge flow rate, cm3 min-1 or m3 s-1 thermodynamic correction factor

LA030258D