Sorption and Diffusion of n-Pentane in Pellets of 5A Zeolite

Georgina C. Laredo , Edith Meneses , Jesús Castillo , Jesús O. Marroquin and Federico Jiménez-Cruz. Energy & Fuels 2008 22 (4), 2641-2648. Abstract | ...
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Ind. Eng. Chem. Res. 1997, 36, 493-500

493

Sorption and Diffusion of n-Pentane in Pellets of 5A Zeolite Jose´ A. C. Silva and Alı´rio E. Rodrigues* Laboratory of Separation and Reaction Engineering, Faculty of Engineering, University of Porto, 4099 Porto Codex, Porto, Portugal

Sorption and diffusion of n-pentane in pellets of 5A zeolite (Rhone-Poulenc) have been studied by gravimetric and ZLC techniques between 373 and 573 K and at partial pressures up to 0.6 bar. Adsorption isotherms were satisfactorily described by a localized adsorption model developed by Nitta et al. (1984) with only one temperature-dependent parameter (coefficient of Henry’s law). The isosteric heat of adsorption is around 12.5 kcal/mol. Kinetic data clearly show that macropore diffusion is the controlling mass-transfer mechanism. Between 473 and 573 K, pore diffusivities range from 0.10 to 0.14 cm2/s in the system He-n-C5 and from 0.07 to 0.09 cm2/s in the system N2-n-C5. Introduction One of the first industrial adsorption processes based on 5A zeolites was the separation n/i-paraffins developed by Union Carbide for the octane improvement of gasoline pools (Symoniak, 1980). The 5A zeolite excludes branched paraffins and adsorbs linear n-C5 and n-C6. The successful application of zeolites as industrial sorbents depends on the appropriate development of sorption-desorption cycles (Barrer, 1981), and this requires an intensive study of phenomena like equilibria and kinetics of adsorption. This research work deals with experimental and modeling studies of equilibria and diffusion of n-pentane in commercial adsorbents of 5A zeolite used in the n/iparaffins separation process. Even if this is not a new subject, the efforts of the scientific community to understand adsorption phenomena make available each year new ways of interpreting adsorption and new experimental techniques. Adsorption equilibrium isotherms can be analyzed from a thermodynamic point of view using virial isotherms (Kiselev, 1971; Doetsch et al., 1974; Barrer, 1981; Vavlitis et al., 1981; Ruthven and Kaul, 1996), molecular models based on localized adsorption (e.g., Langmuir, 1918; Nitta et al., 1984; Martinez and Basmadjian, 1996), and empirical correlations (Yang, 1987). Kinetics of sorption in bidisperse porous adsorbents generally includes macropore and micropore diffusion, that could play a role together in mass transfer. Ruckenstein et al. (1971) developed a bidisperse pore model for transient diffusion in bidisperse porous adsorbents, assuming that both resistances are in series, and Ruthven and Loughlin (1972) developed a criterion for the relative importance of the two phenomena based on that model. The model was used in the interpretation of gravimetric experimental sorption rates by Ruckenstein et al. (1971) and Ruthven et al. (1986). More recently Eic and Ruthven (1988) developed a straigthforward technique for measuring transport diffusivities in zeolite crystals: the ZLC (zerolength-column) method. The extension to the study of diffusivities in pellets was made by Ruthven and Xu (1993). A complete model including macropore and micropore diffusion in pellets applied to the ZLC technique has been recently developed by Brandani (1996), and Silva and Rodrigues (1996) who also suggested recipes for data treatment. * To whom correspondence should be addressed. Email: [email protected]. Telephone: 351 2 2041671. Fax: 351 2 2041674. S0888-5885(96)00477-0 CCC: $14.00

Figure 1. SEM photograph of a Rhone-Poulenc pellet (magnified 4000×).

This work was carried out in the framework of a project on n-pentane/i-pentane separation with 5A zeolites (Rodrigues et al., 1996). The objectives of the first part of the work are the measurement of adsorption equilibrium isotherms of n-C5 in pellets of 5A zeolites by gravimetric techniques and the measurement of diffusivities by ZLC and gravimetric methods. These results will be used later in the modeling of fixed bed adsorption and design of cyclic PSA/VSA processes. Experimental Section Materials and Reagents. The adsorbent is extrudate 5A zeolite 1/16 in. cylindrical pellets (Rhone-Poulenc, France) with length ≈6 mm. The SEM analysis of the pellet shown in Figure 1 reveals that the crystals have a mean cube side of 2 µm. Mercury porosimetry studies performed in our laboratory are reported in Table 1. In some ZLC experiments pellets of the same size but a crystal size of 3.6 µm were also used. The n-pentane is 99% purity (Merck, Germany). Nitrogen and helium are type R and N50, respectively, in AirLiquide (France) classification. Gravimetric Apparatus. The studies of equilibrium and rate of adsorption were performed in the gravimetric apparatus sketched in Figure 2. It has three major sections: weighing system, gas mixing system, and data acquisition. Weighing measurements were performed with a flow C. I. Electronics (U.K.) microbalance (A) in which a cage with pellets inside is suspended in one of his arms (B). In all experiments four pellets were put in the cage, which corresponds to © 1997 American Chemical Society

494 Ind. Eng. Chem. Res., Vol. 36, No. 2, 1997 Table 1. Mercury Porosimetry Results in Rhone-Poulenc Pellets of 5A Zeolite intrusion volume (cm3/g) apparent density, Fa (g/cm3) solid density, Fs (g/cm3) porosity, p

0.24 1.45 2.22 0.35

approximately 50 mg of hydrated sample. A Termolab (Portugal) oven (D) with a type K thermocouple at sample level (E) is monitored with a Shimadzu (Japan) PID controller (F). Flow of adsorbate plus inert always passes down the cage of pellets. Stream 1, inert plus adsorbate, was produced by bubbling nitrogen or helium in liquid adsorbate contained in a Scott (Germany) saturator (wb) immersed in a Techne (U.K.) thermostated bath (TB). The mixture produced could be further diluted by pure inert stream 2. Flow rates of streams 1 and 2 were established by Teledyne-Hastings (Hampton, VA) mass flowmeters (FM) with the corresponding control unit (FMC). Before entering the microbalance, total flowrate and partial pressure are checked in a soap bubble flowmeter (BS). The electrical signal produced in the microbalance by weight changes is sent to a Robal C. I. Electronics control unit (R) and then to a Data Translation (Marlboro, MA) acquisition data board attached to a IBM PS/2 computer (Com). Procedure for Gravimetric Runs. The zeolite sample was dehydrated by heating it from ambient temperature to 633 K in 20 mL/min pure nitrogen or helium over a period of at least 16 h. In the first step of a typical adsorption run, the inert stream 4 is switched to a preset mixture of paraffin and inert (stream 1 plus stream 2). Once the balance achieved a constant weight, valve 2 is closed and 3 opened and another partial pressure of paraffin is established changing stream 1 and 2 ratios. Once the flowrate is constant in a soap-bubble flowmeter, another run is obtained by switching again valves 2 and 3. ZLC Apparatus. ZLC studies were performed in the apparatus shown in Figure 3. The section components are practically the same as those in the gravimetric one only the microbalance is replaced by a gas chromatograph. Pellets, generally three, are placed inside a small column (ZLC) directly attached to the FID GC (Carlo Erba GC 6000 vega series, Italy). Column saturation (stream 3) and purging (stream 4) were performed by two complete separate lines in order to avoid extraneous parasitic effects such as condensation on tube walls and inaccurate definition of zero time in the system (if purge gas passes by the same saturation line, pellet contact with purge gas at zero time could not be made with a free sorbate gas). Procedure for ZLC Technique. Sample dehydration was performed as in the gravimetric technique. Saturation of adsorbent was made with a very small partial pressure (≈4 × 10-3 bar) of n-C5 so adsorption is in the linear region of the isotherm. A typical experiment follows: after saturating the adsorbent with stream 3, streams 3 and 4 are switched in the column, closing on-off valves 2 and 5 and opening 4, and the signal produced by the FID is recorded; at the same time needle valve 2′ is opened a little to permit some backflux of stream 3. Results and Discussion Equilibrium Isotherms. Figure 4 shows n-pentane experimental adsorption equilibrium isotherms on 5A

zeolite pellets. Measurement of the total loading of adsorbent was not possible since data were not reliable at temperatures lower than 373 K. At temperatures higher than 573 K another parasitic effect becomes important: an abnormal increase in weight occurs which does not correspond to physical adsorption because the initial weight of the sample was not recovered in the desorption step; also the sample color changes. Probably some coking occurs. The isosteric heat of adsorption, qst, versus sorbate concentration, Cs, is shown in Figure 5. The values of qst were calculated by

qst ) RT2

ln p (∂ ∂T )

Cs

(1)

where T is the absolute temperature, p is the partial pressure of sorbate, and Cs is the concentration of sorbate in the adsorbed phase. The isosteric heat of adsorption is around 12.5 kcal/mol, which is close to published data by Ruthven (1984) and Vavlitis et al. (1981). A suitable isotherm for a perfect gas in the gas phase at equilibrium with sorbed gas, from a thermodynamic point of view, is the virial isotherm (Kiselev, 1971; Barrer, 1981)

H)

Cs exp(2A1Cs + (3/2)A2Cs2 + (4/3)A3Cs3 + ...) p (2)

where H is the Henry’s law coefficient and A1-3 are virial coefficients. According to the virial isotherm, semilog plots of p/Cs vs Cs extrapolated to zero concentration give us Henry’s constants, which are useful to check the consistency of molecular model isotherms. Figure 6 shows semilog plots of p/Cs vs Cs for the experimental isotherms. Extrapolation is possible in the range of temperature 473-573 K but not at lower temperatures because high adsorbent loadings at small partial pressures of sorbate make extrapolation difficult. Table 2 summarizes Henry’s coefficients obtained from extrapolation of data plotted in Figure 6 to zero concentration. It also includes Vavlitis et al. (1981) data for n-pentane sorption in single crystals of 5A zeolite for comparison with this work. Values of qst according to a van’t Hoff dependence of Henry’s constants with temperature (H ) k0 exp(-qst/RT)) are also shown in Table 2. The virial isotherm is suitable for interpreting data from a thermodynamic point of view but does not give insight into sorption events at the molecular level (Barrer, 1981). Because information concerning multicomponent adsorption will be needed in the future, we decided to model the equilibrium data. For type I isotherms in IUPAC classification a suitable isotherm is represented by the Langmuir (1918) equation

Keq )

1 θ p1-θ

(3)

where θ ) Cs/Cs,max is the degree of filling of sites, Keq is an equilibrium constant, and Cs,max is the maximum concentration of adsorbate at the saturation of the adsorbent. As stated previously, experimental determination of Cs,max was not possible. According to Doetsch et al. (1974), 5A zeolite can accommodate two molecules of n-C7 in its cavities and, according to Ruthven (1984), five molecules of n-C3. For n-C5 this value could be three or four molecules. According to Ruthven (1984), 1 molecule/cavity ) 0.45 mmol/gLinde corresponding to three molecules of n-C5 at 9.75 gn-C5/

Ind. Eng. Chem. Res., Vol. 36, No. 2, 1997 495

Figure 2. Schematic drawing of an experimental gravimetric apparatus for measuring equilibrium and kinetics of sorption: (A) microbalance; (B) cage with pellets; (BS) bubble soap; (Com) computer; (D) radiant oven; (e) thermocouple; (F) PID control of oven; (FM) flowmeter; (FMC) flowmeter control unit; (m) pressure manometer; (R) microbalance control unit; (U) gas exhaust; (TB) thermostated bath; (wb) wash bottle; (1, 2, 3, 4, 5) on-off valves; (1′, 2′) needle valves.

100 gads and to four molecules at 13 gn-C5/100 gads. Looking at Figure 4, the isotherm plateau at 373 K is located at almost 9.7 gn-C5/100 gads; assuming that the zeolite accommodates one more molecule when decreasing the temperature or increasing the partial pressure, a reasonable value for adsorbent saturation is 4 molecules/cavity. A plot of θ/p(1 - θ) against θ according to the Langmuir equation with Cs,max ) 13 g/100 g is shown in Figure 7a; if Langmuir’s equation is valid, a straight line parallel to the θ axis is obtained, with intercept at zero loading that gives the equilibrium constant, which, in turn, multiplied by Cs,max gives Henry’s law coefficient. It can be seen that the Langmuir equation does not represent well the experimental data. More recently Nitta et al. (1984) developed an equilibrium adsorption isotherm which is similar to the Langmuir one. They assumed localized adsorption in which the adsorbed molecule occupies a certain number of active sites, n. The isotherm expression is, neglecting the interaction term between adsorbed molecules in the original model:

Keq )

θ 1 p (1 - θ)n

(4)

where n is the number of active sites occupied by an adsorbed molecule. According to Nitta et al. (1984) θ ) Cs/Cs,max with Cs,max ) As/n, where As is the total number of active sites in the adsorbent. According to Nitta et al. (1984), the total number of active sites in 5A zeolite

is on the order of 9 mmol/g. If n ) 5, we obtain Cs,max ) 1.8 mmol/g which corresponds to exactly 4 molecules/ cavity. This value is acceptable as mentioned above. With n ) 5 and Cs,max ) 13 g/100 g only Keq is unknown in eq 4. Model validation follows the same pattern of the Langmuir isotherm; in a plot θ/p(1 - θ)n vs θ all isotherms should be straight lines parallel to the θ axis; Keq are the intercepts at zero loading. Figure 7b shows a plot of θ/p(1 - θ)5 against θ and Figure 4 the Nitta et al. model superimposed to experimental data. Henry’s law coefficients obtained by the intercept at zero loading in Figure 7b are shown in Table 2; they range from 0.28 to 144 gn-C5/gads‚bar between 573 and 373 K, respectively. Figures 4 and 7b clearly show that results predicted by the Nitta et al. model are in good agreement with experimental data. All parameters calculated in a straightforward way have physical meaning, and only Henry’s law coefficient is temperature dependent. The model of Nitta et al. can be extended to multicomponent systems and could predict azeotropes as pointed out by Sircar (1995) and Martinez and Basmadjian (1996), so in the future we will test this model in multicomponent systems. Kinetics of Sorption In bidisperse porous adsorbents such as zeolite pellets there are two diffusion mechanisms: the macropore diffusion with time constant Dp/Rp2 and the micropore diffusion with time constant Dc/rc2. Assuming that the diffusion mechanisms are in series, Ruckenstein et al.

496 Ind. Eng. Chem. Res., Vol. 36, No. 2, 1997

Figure 3. Schematic drawing of an experimental ZLC apparatus for measuring sorption kinetics: (BS) bubble soap; (Com) computer; (Cr) chromatograph; (FID) detector of chromatograph; (FM) flowmeter; (FMC) flowmeter control unit; (m) pressure nanometer; (TB) thermostated bath; (U) gas exhaust; (wb) wash bottle; (zlc) zero-length column; (1, 2, 3, 4, 5) on-off valves; (1′, 2′) needle valves.

(1971) developed a bidisperse porous model applied to the measurement of transient diffusion. On the basis of such a model, Ruthven and Loughlin (1972) developed a criterion to the relative importance of the diffusion mechanisms which is given by γ:

γ)

Dc/rc2(1 + K) Dp/Rp2

(5)

where K ) (1 - p)Had/p is the capacity factor and Had ()FsRTH/Mw) is the dimensionless Henry’s constant or local slope of the isotherm. Macropore diffusivity is the controlling mechanism for γ > 10; crystal diffusivity is the controlling mechanism for γ < 0.1; if 0.1 < γ < 10, both macropore and crystal diffusivity should be taken into account. For the present system an estimate of the relative importance of diffusional resistances can be made. For example at 573 K, Dm(He-n-C5) ≈ 1 cm2/s; assuming tortuosity Tp ) 4 and particle porosity p ) 0.35 as common values in a zeolite pellet, the capacity factor K calculated in the linear region of the isotherm is K ) 760; for a pellet with radius Rp ) 0.08 cm the apparent time constant for diffusion in macropores will be Dp/ Rp2(1 + K) ) 0.05 s-1. For micropore diffusion it is more difficult to obtain representative data because very different values are reported. Ruthven (1984) reported a value of Dc/rc2 ≈ 0.18 s-1 for sorption of n-C5 in 5A zeolite at 523 K with crystals of 3.6 µm; the activation energy for diffusion of C5 paraffins in 5A zeolite (Cav-

Figure 4. Adsorption equilibrium isotherms of n-pentane in pellets of 5A zeolite. Points are experimental results. Calculated isotherms from the Nitta et al. model (s) are also shown. Absolute temperatures are quoted in each curve.

alcante et al., 1995) is on the order of 5 kcal/mol, which gives at 573 K, with rc ) 1 µm, Dc/rc2 ≈ 0.09 s-1. With this value γ is equal to 1.8, suggesting a system dominated by both diffusion resistances. In the work of Cavalcante et al. (1995) a value of Dc ≈ 1 × 10-8 cm2/s at 573 K is shown for a C5 paraffin in 5A zeolite, from which we calculate Dc/rc2 ≈ 1 s-1 originating γ ) 20, suggesting a macropore control system. Therefore, no conclusion concerning the controlling diffusion mechanism can be drawn from previous data. In bidisperse porous adsorbents, it is important to carry out experiments in pellets with different sizes but

Ind. Eng. Chem. Res., Vol. 36, No. 2, 1997 497

Figure 5. Dependence of isosteric heats of adsorption with coverage.

Figure 6. Semilog plot of p/Cs vs Cs for analysis of virial isotherm.

Figure 7. Semilog plot of θ/p(1 - θ)n vs θ for adsorption of n-pentane in pellets of 5A zeolite: (a) n ) 1 (Langmuir isotherm); (b) n ) 5 (Nitta et al. isotherm).

Table 2. Henry’s Coefficients and Isosteric Heats of Adsorption Calculated from Virial Isotherm and Nitta et al. Model (1984) According to Experimental Data of This Worka

temperature (K) 674 617 573 568 523 473 423 373 qst (kcal/mol)

virial isotherm (this work) H (g/g‚bar)

Nitta et al. isotherm (this work) H (g/g‚bar)

virial isotherm (Vavlitis et al., 1981)b H (g/g‚bar) 0.07 0.15

0.25

0.28

0.77 2.5

0.82 3.2 16 144

12.4

13.2

0.33 0.81

11.6

a

Comparison with previous results of Vavlitis et al. (1981) obtained from the virial isotherm. b We consider 1 molecule/cavity ) 0.45 mmol/gLinde (Ruthven, 1984).

with the same crystal size (different Rp, same rc) or pellets with the same size but with different crystals (same Rp, different rc). If macropore diffusion is controlling, time constants for diffusion should depend directly on pellet size and should be insensitive to crystal size changes. If micropore diffusion controls, the reverse is true. Effect of Purge Gas and Purge Flowrate on ZLC Desorption Curves. Parts a and b of Figure 8 show the effect of purge flowrate on desorption curves at 573 K obtained by the ZLC technique for the systems N2n-C5 and He-n-C5, respectively. It is apparent from the figures that desorption curves are sensitive to the nature of purge gas; desorption in the system He-n-C5 is faster than that in the system N2-n-C5. This is an indication that micropore diffusion is not the total resistance in the system, but no information concerning the controlling mechanism can be drawn.

Figure 8. Effect of purge flowrate and purge gas in semilog plots of Cout/C0 vs t obtained in the ZLC system: (a) N2-n-C5 at 573 K; (b) He-n-C5 at 573 K.

Effect of Crystal Size on ZLC Desorption Curves. The effect of crystal size on desorption curves in the system He-n-C5 is shown in Figure 9; experiments are carried out with the same pellet size. Desorption curves

498 Ind. Eng. Chem. Res., Vol. 36, No. 2, 1997

pellets as an infinite cylinder, from which the relevant solution for the ZLC model in a macropore control system is (Crank, 1975)

Cout C0

) 2L

∞

exp(-βn2Dpt/Rp2(1 + K))

n)1

(βn2 + L2)

∑

(6)

where

Figure 9. Effect of crystal size in pellets at 573 K in the system He-n-C5: semilog plot of Cout/C0 vs time t in the ZLC system.

βnJ1(βn) - LJ0(βn) ) 0

(7)

2 1 purge flowrate Rp L) 2 pellets volume pDp

(8)

where Cout is the outlet concentration of the ZLC cell, C0 is the concentration at time zero in the ZLC cell, βn are roots of transcendental equation (7), and J1(βn) and J0(βn) are Bessel functions of the first kind. According to Eic and Ruthven (1988), an easy way to determine model parameters is to use the information of desorption curves at long times. Model series represented in eq 6 at long times reduces to

( ) (

ln

)

Cout β12Dpt 2L ) ln 2 C0 β1 + L2 Rp2(1 + K)

(9)

The experimental intercept and slope of straight lines at long times in the semilog plots of desorption curves seen in Figures 8-10 are related to eq 9. Using intercept and slope information in conjunction with the definition of parameter L, the relevant equations to obtain model parameters are

2L ) Intercept; 2 β1 + L2

β12Dp

-

) Slope; Rp2(1 + K) pDp 1 purge flowrate L 2 ) 2 pellets volume R p

Figure 10. Effect of temperature on desorption curves in the system N2-n-C5: semilog plot of Cout/C0 vs time t in the ZLC system.

are insensitive to crystal size variations, so it is clear that the controlling resistance to mass transfer is the macropore diffusion. Effect of Temperature in ZLC Desorption Curves. The effect of temperature on desorption curves for the system N2-n-C5 is shown in Figure 10, revealing a strong temperature dependence of desorption time (which can be erroneously interpreted as an activated diffusion with activation energy on the order of the heat of adsorption), indicating clearly macropore diffusion control. According to these results, a model for ZLC desorption curves taking into account only macropore diffusion is the relevant one. Assuming pellets and crystals as spheres, that model could be obtained by a limiting form of the ZLC complete model for bidisperse adsorbents developed by Brandani (1996) and Silva and Rodrigues (1996) or starting from the assumption that macropore diffusion is the controlling mechanism as Ruthven and Xu (1993) did. Another approach is to consider the

where Intercept and Slope are experimental information. Another way was to use the experimental values of the intercept and slope represented in eq 9 and the transcendental equation (7). The two methods should give the same parameters. Model parameters calculated by the first procedure are summarized in Table 3 for the systems He-n-C5 and N2-n-C5 at temperatures 473-573 K. Time constants of diffusion are weakly temperature dependent, which is consistent with a macropore diffusion control; however, apparent time constants for diffusion defined by Dp/Rp2(1 + K) plotted vs 1/T in Figure 11 for the system He-n-C5 are strongly temperature dependent with an activation energy of 13.8 kcal/mol which is on the order of the heat of adsorption 12.5 kcal/mol. Time constants range from 0.002 s-1 at 473 K up to 0.03 s-1 at 573 K. In order to check if the gravimetric technique leads to similar results obtained by ZLC, gravimetric experiments in similar conditions of the ZLC were performed. The adsorbent was saturated with a small partial pressure of paraffin (≈4 × 10-3 bar) in order to ensure the validity of Henry’s law and desorbed with a high purge flowrate (near 600 mL/min STP). Assuming that the model representating the ZLC apparatus can be

Ind. Eng. Chem. Res., Vol. 36, No. 2, 1997 499 Table 3. Summary of Experimental Conditions and Model Results of Diffusion Parameters in the ZLC Technique Q (mL/min)

intercept

-slope (s-1)

24 36 50 100

System N2-n-C5 Temperature 573 K 0.86 0.026 0.69 0.03 0.57 0.036 0.33 0.048

24 36 70 120

0.79 0.66 0.41 0.23

Temperature 523 K 0.010 0.012 0.014 0.018

24 36 130

0.75 0.52 0.17

Temperature 473 K 0.0034 0.0038 0.0060

15 30 50

System He-n-C5 Temperature 573 K 1 0.030 0.80 0.040 0.69 0.050

40

0.68

Temperature 523 K 0.020

30 60

0.60 0.47

Temperature 473 K 0.0055 0.0070

τdif (s)

L

β1

0.18 0.20 0.20 0.20 avg 0.20

1.1 1.9 2.7 5.6

1.2 1.4 1.5 1.8

0.21 0.21 0.22 0.24 avg 0.23

1.3 2.0 4.3 8.2

1.3 1.4 1.6 1.9

0.22 0.30 0.31 avg 0.28

1.3 2.4 11

1.3 1.7 2.2

0.13 0.14 avg 0.13

1.0 1.8

1.2 1.4

1.5 3.1

1.6 1.8

Figure 11. Apparent time constant of diffusion Dp/Rp2(1 + K) vs 1/T for the gravimetric and ZLC systems.

0.15 0.20 0.19 avg 0.19

applied to the gravimetric technique, the relevant solution is (Crank, 1975)

Mt M0

2

) 4L

∞

exp(-βn2Dpt/Rp2(1 + K))

n)1

βn2(βn2 + L2)

∑

(11)

where Mt is the amount of sorbate in the pellet at time t, and M0 is the amount of sorbate in the pellet at time zero. If L f ∞, then eq 11 reduces to (Crank, 1975)

Mt M0

∞

)4

∑

Figure 12. Effect of temperature in uptake desorption curves in the system He-n-C5 obtained by the gravimetric technique. Table 4. Experimental and Predicted Pore Diffusivities temp (K)

1

n)1β

2

2

2

exp(-βn Dpt/Rp (1 + K))

(12)

n

where βn are calculated from J0(βn) ) 0. For more than 70% uptake only the first term is relevant and the model reduces to

( ) ( )

Mt β12Dpt 4 ln ) ln 2 - 2 M0 β1 Rp (1 + K)

(13)

In order to apply eq 13, experimental data of Mt/M0 vs time t in a semilog plot should be a straight line at long times with slope -β12Dp/Rp2(1 + K) and intercept 4/β12. Figure 12 shows the effect of temperature on desorption curves obtained with a high purge flowrate of helium in order to guarantee a high value of L to validate eq 13. Desorption curves are well described by the theory outlined above. The apparent time constants of diffusion Dp/Rp2(1 + K) calculated from the long time slopes in Figure 12 are represented in Figure 11; they range from 0.0016 s-1 at 473 K to 0.024 s-1 at 573 K. Both techniques gave the same order of temperature dependence in apparent time constants of diffusion; however, the values obtained by gravimetry are slightly smaller

τdif (s)

Dp,exp (cm2/s)

Dm (cm2/s)

573 523 473

0.20 0.23 0.28

System N2-n-C5 0.09 0.27 0.08 0.24 0.07 0.21

573 523 473

0.13 0.15 0.19

System He-n-C5 0.14 1.0 0.12 0.87 0.10 0.75

DK (cm2/s)

Tp

0.27 0.26 0.25

1.5 1.5 1.6

0.27 0.26 0.25

1.5 1.6 1.8

than those obtained by the ZLC technique. The results obtained by gravimetric and ZLC techniques show that, at low adsorbent loadings, the macropore diffusion time constant controls the mass transfer in the systems Hen-C5 and N2-n-C5. Diffusion mechanisms in macropores are Knudsen diffusivity in series with molecular diffusion, and so the pore diffusivity is

Dp )

1 1 1 Tp + Dm DK

{

}

(14)

In Table 4 we summarize the values of experimental pore diffusivity Dp (obtained from values of τdiff in Table 3), Knudsen diffusivity DK (average pore size of 0.1 µm as in Rodrigues et al. (1996)), molecular diffusivity Dm

500 Ind. Eng. Chem. Res., Vol. 36, No. 2, 1997

(estimated by the Chapman-Enskog equation), and tortuosity factors Tp predicted by eq 14. The values of Tp are similar in both systems and do not change with temperature, suggesting that eq 14 represents with good accuracy the macropore diffusion mechanisms of this system. Conclusions A detailed study of adsorption and diffusion of npentane in commercial pellets of 5A zeolite was performed. The adsorption equilibrium was interpreted with a model of localized adsorption in a homogeneous surface, assuming that a molecule when adsorbed occupies a certain number of active sites with no interaction between sorbed molecules. Mass transfer in the pellet was dominated at low loadings of the adsorbent by macropore diffusion. This conclusion was confirmed by two independent experimental techniques, namely ZLC and gravimetry. The pore diffusivity of n-C5 in pellets of 5A zeolite ranges from 0.07 to 0.09 cm2/s when temperature changes from 473 to 573 K in N2 carrier gas; for the system He-n-C5 the pore diffusivity in the same temperature range varies from 0.10 to 0.14 cm2/s. Acknowledgment J.A.C.S. acknowledges financial support from Junta Nacional de Investigac¸ a˜o Cientı´fica e Tecnolo´gica (Research Fellowship; Praxis XXI/BD/94). Nomenclature A1-3 ) virial coefficients Cs ) sorbed phase concentration (mol/cm3) Cout ) outlet concentration in a ZLC cell (mol/cm3) C0 ) concentration at time zero in the pellet (mol/cm3) Dc ) diffusion in crystals (cm2/s) DK ) Knudsen diffusion (cm2/s) Dm ) molecular diffusion (cm2/s) Dp ) diffusion in macropores (cm2/s) H ) Henry’s law coefficient (ggas/gads‚bar) Had ) dimensionless Henry’s law coefficient ()FsRTH/Mw) J0(βn) ) Bessel function of first kind and order 0 J1(βn) ) Bessel function of first kind and order 1 K ) capacity factor, dimensionless Keq ) equilibrium constant (bar-1) L ) ZLC operation parameter defined by eq 7, dimensionless M0 ) amount of sorbate in the pellet at time zero (mol/ cm3) Mt ) amount of sorbate in the pellet at time t (mol/cm3) Mw ) molecular mass of sorbate (g/mol) p ) partial pressure of sorbate (bar) qst ) isosteric heat of adsorption (kcal/mol) R ) ideal gas law constant (cm3‚bar/mol‚K) rc ) crystal radius (cm) Rp ) pellet radius (cm) T ) absolute temperature (K) Tp ) tortuosity

τdif ) time constant for diffusion in macropores ()Rp2/pDp) (s) γ ) ratio of macropore and micropore diffusion time constants, dimensionless

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Received for review August 2, 1996 Revised manuscript received November 12, 1996 Accepted November 14, 1996X

Greek Symbols βn ) roots of transcendental equation (7) θ ) fractional coverage of adsorbent, dimensionless p ) macropore porosity Fs ) solid density (g/cm3) Fa ) apparent density of solid (g/cm3)

IE960477C

Abstract published in Advance ACS Abstracts, January 1, 1997. X