Ind. Eng. Chem. Res. 1999, 38, 2051-2057
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Adsorption Equilibria and Kinetics for Propylene and Propane over 13X and 4A Zeolite Pellets Francisco A. Da Silva and Alı´rio E. Rodrigues* Laboratory of Separation and Reaction Engineering, Faculty of Engineering, University of Porto, 4099 Porto Codex, Portugal
Propylene and propane single-adsorption equilibrium isotherms and mass-transfer kinetics over 13X and 4A zeolite pellets have been investigated using gravimetry and zero length column techniques, respectively. The 13X zeolite shows a higher loading capacity and lower mass-transfer resistance while 4A zeolite shows the highest selectivity for propylene. The experimental adsorption equilibrium isotherms were adjusted with the Toth isotherm. Kinetic studies indicate that macropore diffusion controls the mass transfer inside 13X zeolite pellets while micropore diffusion controls the propylene adsorption on 4A zeolite pellets. Introduction
Table 1. Main Physical Properties of Commercial Zeolites Evaluated
Propylene/propane gas separation is an important issue in the petrochemical industry because it is one of the most demanding energetic separation processes. The relative volatility of this system1 is between 1.0 and 1.1 at temperatures in the range of 244-327 K and total pressures of 1.7-22 bar. Consequently, if traditional distillation is used, more than 100 theoretical plates are needed when high-purity propylene is required as a product (>99.5% mole fraction). Hybrid methods which combine traditional distillation and adsorption processes have been proposed as a valid alternative.2-5 In order to achieve that objective, it is important to find a selective adsorbent able to perform the separation based on selective equilibrium or different kinetics. In that case the commercial zeolites6,7 and some Ag+-substituted resins8,9 appear to be important options. However, it is found that solid regeneration is difficult to accomplish during the blowdown steps10 or the large masstransfer resistance leads to long step cycles when a vacuum swing adsorption (VSA) process is implemented,11 at temperatures as low as 298 K. The aim of this work is to present experimental single-adsorption isotherms and kinetic data for propylene and propane over commercial 13X and 4A zeolites at temperatures between 373 and 473 K, where the information found in the literature is relatively scarce. At these temperatures the problems of equilibrium irreversibility and mass-transfer resistances are reduced, but selectivity and capacity are reduced too and coke deposition over the solid sorbent can occur. The trade-off among these effects will determine the best operating conditions to perform the propylene/propane separation by adsorption using commercial zeolites. The adsorption isotherms are obtained by the gravimetric method while the adsorption kinetics is studied using the zero length column (ZLC) technique. The experimental work is carried out directly with the commercial zeolite pellets where the ZLC method is applied in two limiting cases: the macropore control system (13X zeolite) and the micropore control system (4A zeolite). * To whom correspondence should be addressed. E-mail:
[email protected]. Telephone: 351 2 2041671. Fax: 351 2 2041674.
property
4A Rhoˆne-Poulenc 13X CECA
extrudate diameter, mm length of the extrudate, mm bulk density, kg/m3 water adsorption capacity, wt % crystal diameter, µm pellet porosity, pellet density, kg/m3 solid density, kg/m3
3.2 8-12 >700 ∼22 3.4 0.34 1700 2590
1.5-1.9 4-7 630-680 21-24 2.0 0.39 1358 2234
Experimental Work and Methodology for Analysis of Results Single-Adsorption Equilibrium Isotherms. The single-adsorption isotherms were obtained with a microbalance (CI-Robal, Wilshire, U.K.) operated in a closed system mode. A small amount of 13X or 4A zeolite (60-75 mg humid sample) in a pellet form was introduced in the microbalance basket, and the sample was submitted to a controlled temperature ramp of 0.4-0.5 K/min in vacuum conditions (total pressure of ∼1 mbar) until 593 K was reached. The sample was kept at 593 K and 1 mbar for 5-6 h until no further variations in the weight were detected. The samples lost nearly 20% of their weight during this procedure while releasing the humidity adsorbed. The temperature of the singleadsorption isotherm is fixed in the oven, and the system is kept waiting until steady conditions are achieved. The experimental isotherm starts from the vacuum condition until nearly 1 bar (adsorption path), introducing small amounts of the sorbate step by step. Once the atmospheric pressure is reached, the opposite trajectory (desorption path) is followed until the initial low pressure is achieved. The weight differences and pressure increments are recorded during all experimental cycles. Single-adsorption equilibrium isotherms at 303, 323, 343, 373, 423, and 473 K were measured for the 13X zeolite and at 303, 343, 383, 423, and 473 K for the 4A zeolite using this procedure. Helium 50 (>99.999%) and nitrogen 45 (>99.995%) were used as inert gases during the regeneration procedure, while the purity of the sorbate gases used was N24 for propylene (>99.4%) and N35 for propane (>99.95%); all gases were provided by Air Liquide. Representative characteristics of the zeolite samples are reported in Table 1.
10.1021/ie980640z CCC: $18.00 © 1999 American Chemical Society Published on Web 04/10/1999
2052 Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999 Table 2. Limiting ZLC Models for the Macropore and Micropore Mass-Transfer Controlled Regimes
The single-adsorption isotherms were fitted with12 the Toth model:
n°i )
mbiP°i [1 + (biP°i)ki]1/ki
(1)
where n°i is the adsorbed amount of the single component i, m is the maximum loading capacity of the sorbent, bi ) bi,0 exp(q/i /RT) is the affinity parameter of the single component i for the solid sorbent, and ki(T) ) Ai + BiT is the solid heterogeneity parameter.13 Mass-Transfer Kinetics via the ZLC Method. The ZLC method is an experimental technique to measure the intraparticle diffusivities in gas/solid systems.14 This method consists of two steps: (1) During the first step, a small amount of a sample is exposed to a diluted stream of a single component in an inert gas (helium or nitrogen). During this step the partial pressure of the single component is kept constant at a fixed temperature until the sample is saturated. (2) In the second step, the cell is cleaned with pure inert gas at a fixed flow rate, at the same temperature of the previous step, and a signal proportional to the sorbate concentration in the bulk gas fluid is recorded, generally in a flame ionization detector (FID). This signal constitutes a desorption experimental curve C(t)/C0 of the ZLC cell which is then compared with an analytical model where the pore and/or crystal diffusivities are the main parameters to be calculated. The ZLC technique has the advantage of allowing a straight calculation of diffusivities, in particular when one of the mass-transfer resistances (macropore or micropore) is dominant. When working in the Henry’s law region and under isothermal conditions, the mass balances around the pellet and the overall system can be solved together and the analytical solution is obtained.15 The main assumptions to obtain the ZLC mathematical desorption model are as follows: (a) Gas behavior is ideal. (b) The process is isothermal. (c) The adsorption isotherm of a single component follows Henry’s law. (d) The external film mass-transfer is negligible. (e) The pellet adsorbent is cylindrical while the crystals which constitute the pellet are considered spherical. (f) The ZLC cell works as a perfectly mixed tank. The model equations for the limiting cases when macropore and micropore are the controlling mechanisms are shown in Table 2. The experimental C/C0 curve obtained from the FID is compared with the
analytical expression, where the reciprocal diffusion time constants Kp/(K + 1) or Kc are calculated by a matching procedure. K is the dimensionless sorbent capacity defined in terms of the Henry constant H as K ) (1 - p)FsHRT/p, where p is the pellet porosity, Fs is the solid density, and T is the absolute temperature; C0 ) P0/RT is the initial sorbate concentration. The transient solutions for both models are mathematically equivalent. The main difference is found in the form of the transcendental equations (3) and (5), from which the βi’s should be computed. A straightforward procedure toward a direct calculation of the kinetic parameter is found when the analytical equation at long time intervals is taken,14-19 because then the first term of the series becomes dominant. After plotting the experimental curves in a semilog scale, we obtain the intercept and the slope from which the diffusion constants are calculated. Results and Discussion 13X Zeolite-Propylene/Propane System. Adsorption Equilibria. Parts a and b of Figure 1 show the experimental single-adsorption equilibrium isotherms for propylene and propane. The values obtained with the Toth model are represented with full lines in those figures. Table 3 shows the fitting parameters obtained with the Toth isotherm adjusted over the single experimental data. It can be seen that the Toth isotherm represents nearly well the experimental curves, especially at higher temperatures between 373 and 473 K. At temperatures as low as 303 K, larger deviations are observed, being more important for propane isotherms at lower coverage. A larger capacity for propylene with respect to propane is observed. The selectivity calculated as the ratio spropylene,propane ) bpropylene/bpropane gives an average value of around 10 in the temperature range studied. This value agrees with a selectivity factor between 8 and 10, at temperatures between 298 and 343 K, and a pressure of 1 bar reported by Huang et al.7 The isosteric heat of adsorption calculated with the Clausius-Clapeyron relationship and the Toth isotherm gives 35.8 and 42.5 kJ/mol for propane and propylene, respectively. This indicates that the interaction between propylene and the 13X surface is higher than that between propane and 13X. The isosteric heat of adsorption reported by Loughlin et al.20 for propane over 13X zeolite is 32.9 kJ/mol, while for propylene, the isosteric
Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999 2053
Figure 1. Propylene and propane adsorption isotherms over 13X zeolite CECA. The solid line is the Toth model, with fitting parameters of Table 3.
Figure 2. Effect of flow rate on ZLC curves, C/C0 vs time, at 423 K, using He as the purge gas over 13X zeolite CECA: (a) propylene; (b) propane. Table 3. Fitting Parameters for the Toth Model Applied to Propylene (1)/Propane (2)-Zeolite Single Experimental Isotherms (13X Zeolite from CECA and 4A Zeolite from Rhoˆ ne-Poulenc, Both in Pellet Form) sorbent 13X CECA 4A Rhoˆne-Poulenc
m, mol/kg 2.68 2.03
A1 0.608 0.666
B1, K-1 0.0 0.0
A2 0.580 1.0
Table 4. Characteristic Parameters of the ZLC with 13X Zeolite CECA cell void fraction, b ZLC cell height ZLC cell volume pellet void fraction, p pellet radius, Rp total pellet volume, Vtp solid density, Fs sorbate partial pressure, P0
0.36 19 mm 60 mm3 0.39 0.79 mm 37.9 mm3 2234 kg/m3 ∼0.5 kPa
heat of adsorption calculated from single isotherm data obtained from literature4,6,7,21 is between 46.1 and 52.7 kJ/mol. ZLC Experiments over 13X Zeolite CECA. ZLC experiments were carried out at 393, 423, and 473 K at three different flow rates of purge inert gas (40, 60, and 80 sccm) using helium or nitrogen as the inert gas. Table 4 shows the characteristic parameters for this case. The effect of the gas flow rate over the ZLC runs obtained for propylene and propane over 13X zeolite at 423 K, with He being the inert gas used, is shown in Figure 2a,b. As soon as the purge gas flow rate increases, lower desorption times are obtained as a result of a spacetime reduction of the cell. The propylene curves are also slower than the propane curves at similar operating conditions, which is easily confirmed if the macropore
B2, K-1 0.0 0.0
b0,1, kPa-1
b0,2, kPa-1
10-7
10-7
3.5 × 7.4 × 10-6
3.5 × 6.0 × 10-4
q/1/R, K
q/2/R, K
5100 3594
4300 0
control model is valid and the macropore diffusion time constants are compared in terms of the {Kp/(K + 1)propylene}/{Kp/(K + 1)propane} ratio. Assuming that Kp’s are similar for both propylene and propane, the difference in diffusion constant is mainly determined by the Kpropylene/Kpropane ) spropylene,propane ≈ 10 ratio, impliying that longer experimental ZLC runs for propylene are expected. When Figures 2 and 3 are compared, the effect of the nature of inert gas while purging the cell equilibrated with sorbate at 423 K can been seen. In the first case, He was used while in the second case N2 was used for propylene (case a) and propane (case b), respectively. The experiments carried out with nitrogen are practically two times as slow as those with helium, suggesting that the interaction between propylene and nitrogen is higher than that between helium and propylene. Again this is an indicator that a macropore control process could be the dominant mass-transfer mechanism, as the pellet diffusivity is depending on the nature of the inert gas. Figure 4 shows the effect of temperature on the ZLC runs for propylene and propane over 13X with He as the purge gas with a fixed flow rate of 60 sccm. A strong temperature dependence is observed in both cases, being stronger for propylene. Table 5 shows the pore diffu-
2054 Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999
Figure 3. Effect of flow rate on ZLC curves, C/C0 vs time, at 423 K, using N2 as the purge gas over 13X zeolite CECA: (a) propylene; (b) propane.
Figure 4. Effect of the temperature in ZLC runs for single propylene and propane over 13X zeolite CECA and a He purge flow rate of 60 sccm: (a) propylene; (b) propane. Table 5. Average Experimental Reciprocal Time Constants, Pore Diffusivities, and Tortuosities for Single Propylene and Propane over 13X Zeolite CECA T, K
Kp/(K + 1), s-1
Dp, cm2/s
Dm, cm2/s
393 423 473
0.0071 0.015 0.045
He-C3H6 0.09 0.11 0.16
393 423 473
0.049 0.086 0.22
He-C3H8 0.12 0.14 0.20
Dk, cm2/s
τ
0.77 0.87 1.04
0.41 0.43 0.46
3.0 2.6 2.0
0.71 0.80 0.97
0.41 0.42 0.44
2.2 2.0 1.5
sivities obtained for both sorbates over 13X with He as the purge gas. The Chapman-Enskog equation was used to calculate the molecular diffusivity Dm, which combined in series with Knudsen diffusivity Dk (calculated with an average pore size of 0.3 µm),22 through the Bonsaquet relationship (Dp ) 1/τ{1/Dm + 1/Dk}), allows the calculation of the tortuosity factor τ. The global average tortuosity factor of 2.2 was calculated including the tortuosity factors obtained from the ZLC runs with nitrogen. Another result corroborating that macropore diffusivity is the controlling mechanism is obtained when values of γ are estimated using the crystal diffusivity reported by Brandani23 over the 13X crystals. Values of γ higher than 120 for propane and 4400 for propylene were found. 4A Zeolite-Propylene/Propane System. Adsorption Equilibria. The single-adsorption isotherms for propylene and propane over 4A zeolite Rhoˆne-Poulenc are shown in Figure 5. It can be seen that propane is
Figure 5. Single-adsorption isotherms for propylene and propane over 4A zeolite Rhoˆne-Poulenc.
practically not adsorbed (less than 0.2 mol/kg) while propylene shows a total loading between 0.8 and 1.9 mol/kg at 100 kPa for the same temperature range. This loading capacity is lower than that for 13X zeolite CECA under equivalent conditions. Also in the same figure the fitting results obtained with the Toth isotherm are compared, showing large deviations in the 303-383 K temperature range and better fits at 423 and 473 K. At this temperature range the isotherms obtained were more reversible than those at lower temperatures. The propane isotherm is practically a linear function of the
Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999 2055
Figure 7. ZLC runs of propylene over 4A using He and N2 at 80 sccm as the purge gases.
Figure 6. ZLC runs for propylene over 4A zeolite Rhoˆne-Poulenc at three different purge flow rates of nitrogen at 423 K.
pressure of the single component, and there is no clear influence of temperature. Propane can be considered as an inert gas over the 4A zeolite, because of its very low loading adsorption capacity. These results were expected as a consequence of the molecular sieving effect over propane in the 4A zeolite. The crystal pore size for the 4A zeolite is closer to 4.0 Å at 300 K, and the zeolite cannot adsorb molecules with higher effective diameter.24 The molecular diameter of propane is about 4.3 Å while the propylene diameter is around 4.0 Å. Experimental equilibrium and adsorption/desorption experiments from Ja¨rvelin and Fair6 also showed that propane is practically not adsorbed at 298 K when compared with propylene adsorption at similar conditions. Also Rege et al.9 reported two isotherms at 298 and 393 K showing similar conclusions. The isosteric heat of adsorption calculated from the isotherm data is 29.9 kJ/mol, which compares well with 31 kJ/mol reported by Kubota et al.25 ZLC Experiments of Propylene with 4A Zeolite Rhoˆ ne-Poulenc. Ja¨rvelin and Fair6 discarded the 4A zeolite as the adsorbent because its narrow crystal pore size also restricts partially the propylene mass transfer. The ZLC runs performed at 373, 423, and 473 K for propylene using He as the purge gas confirm this observation. When Figures 4 and 6 are compared at the same temperature (423 K) for propylene and using He as the inert gas, the value of C/C0 ) 0.01 is achieved at nearly 75 s using a purge flow rate of 60 sccm over 13X zeolite CECA, while for 4A zeolite Rhoˆne-Poulenc at the same temperature and flow rate, 600 s is required (interpolating between the curves at 40 and 80 sccm). This is the main drawback of using the 4A zeolite as the sorbent for the propylene/propane system when compared with other sorbents such as 13X zeolite. However, it has the highest selectivity for propylene over propane when the selectivity curves obtained with the Toth isotherm and the fitting parameters of Table 3 are compared, as shown in Figure 8. Figure 7 shows the effect of the type of purge gas over the ZLC experimental curve. Contrary to what was observed over the 13X zeolite CECA, the desorption curve is practically insensitive to the type of purge gas,
Figure 8. Propylene/propane selectivity over 13X and 4A zeolites calculated with the Toth isotherm and fitting parameters of Table 3. Table 6. Characteristic Parameters of the ZLC with 4A Zeolite Rhoˆ ne-Poulenc cell void fraction, b ZLC cell height ZLC cell volume pellet void fraction, p crystal radius, rc pellet radius, Rp total pellet volume, Vtp solid density, Fs sorbate partial pressure, P0
0.82 28.6 mm 455 mm3 0.34 1.7 µm 1.6 mm 83.6 mm3 2590 kg/m3 ∼0.6 kPa
suggesting that macropore diffusion is not the masstransfer control mechanism as in the first case. Using the micropore control model and the long time solution technique and parameters shown in Table 6, values of crystal diffusivities of 2 × 10-12, 9 × 10-12, and 4 × 10-11 cm2/s at 373, 423, and 473 K, respectively, are found. These results compare fairly well with the results of Rege et al.9 and Kubota et al.,25 which in terms of the crystal diffusion constant, Kc, are between 10-4 and 10-3 s-1 in the same temperature range explored here. Also, an approximate value of γ confirms that micropore control is the dominant mechanism for this system. Assuming that Kp has a value similar to that found for 13X CECA experiments (larger than 8 s-1), γ values between 0.04 and 0.11 are calculated between 373 and
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473 K, suggesting that crystal diffusivity is the controlling mass-transfer mechanism for this system. Conclusions Two commercial adsorbents, 13X and 4A zeolite, were studied as candidates to carry out the propylene/ propane separation by adsorption. The 13X zeolite shows higher loading capacity (about 30% when the maximum loading capacity is compared for propylene) and lower mass-transfer resistance than the 4A zeolite as found when the reciprocal time constants are compared, 10-2-10-1 s-1 for 13X zeolite CECA against 10-4-10-3 s-1 for 4A zeolite Rhoˆne-Poulenc, between 373 and 474 K. However, the 4A zeolite selectivity for propylene (100-1000) is at least 1 order of magnitude higher than that of 13X zeolite (∼10) in the same temperature range, which could compensate for the lower capacity and higher mass-transfer resistance of 4A zeolite as the sorbent. The Toth isotherm produces accurate results at higher temperatures for both systems showing a large deviation with respect to the experimental data at lower coverage and low temperature. The macropore diffusion control model is the dominant mass-transfer mechanism over the 13X zeolite as verified for the dependence of the ZLC runs with the nature of the inert purge gas and by the higher values of the γ for both propylene (γ ∼ 4400) and propane (γ ∼ 120). For this system an average tortuosity of 2.2 is obtained. The micropore diffusion is dominant for propylene adsorption over the 4A zeolite, as confirmed by the negligible dependence of ZLC curves on the nature of inert purge gas and lower γ values. Notation bi ) equilibrium parameter for component i, kPa-1 bi,0 ) preexponential constant of the Arrhenius temperature dependence of the bi parameter, kPa-1 C ) molar concentration of the sorbate in the bulk gas phase, mol/m3 C0 ) total molar concentration of the sorbate at P and T ZLC cell conditions, mol/m3 Dc ) crystal diffusion coefficient, m2/s Dk ) Knudsen diffusivity, m2/s Dm ) Binary molecular diffusivity,m2/s Dp ) pore diffusion coefficient, m2/s H ) Henry constant, mol/kg‚kPa J0, J1 ) Bessel functions of the first kind of order 0 and 1 ki ) heterogeneity parameter for the Toth isotherm for the single component i K ) dimensionless loading capacity of the sorbent Kc ) characteristic crystal mass-transfer constant, s-1 Kp ) characteristic pore mass-transfer constant, s-1 L ) ZLC operating parameter in macropore control conditions L′ ) ZLC operating parameter in micropore control conditions m ) loading saturation coefficient, mol/kg P0, P°i ) partial pressure of component i, kPa q/i ) equilibrium parameter which fixed the exponential temperature dependence of the bi parameter, J/mol Q ) volumetric purge flow rate at ZLC operating conditions, m3/s rc ) crystal radius, µm R ) ideal gas constant ()8.3144), J/mol‚K Rp ) pellet radius, m
si,j ) adsorption selectivity for component i with respect to component j sccm ) standard cubic centimeters per minute, at 273 K and 760 mmHg t ) time, s T ) temperature, K Vtp ) total pellet volume, m3 Greek Letters R, R′ ) ZLC auxiliary variable, s-1 βi ) root of transcendental equations (3) and (5) b ) ZLC void fraction p ) pellet void fraction γ ) ratio of reciprocal micropore and macropore diffusion time constants Fs ) solid density, kg/m3 τ ) tortuosity factor Superscripts ′ ) refers to crystal scale * ) equilibrium ° ) pure component Subscripts b ) cell c ) crystal i, j ) i or j component 0 ) reference condition, characteristic value, initial p ) pellet s ) solid t ) total
Acknowledgment Financial support from PRAXIS XXI/CEG/3/3.1/2644/ 95 is ackowledged. F.A.D.S. acknowledges financial support from Junta Nacional de Investigac¸ ao Cientı´fica e Tecnolo´gica (Research fellowship; Praxis XXI/BD5772/ 95), the technical support of Jose´ Antonio Silva while performing the experimental runs, Vera Mata, who performed the pellet characterization, and Ricardo Guedes at CEMUP. Literature Cited (1) Manley, D. B.; Swift, G. W. Relative Volatility of PropanePropene System by Integration of General Coexistence Equation. J. Chem. Eng. Data 1971, 16 (3), 301. (2) Kumar, R.; Golden, T. C.; White, T. R.; Rokicki, A. Novel Adsorption Distillation Hybrid Scheme for Propane/Propylene Separation. Sep. Technol. 1992, 15, 2157. (3) Eldridge, R. B. Olefin/Paraffin Separation Technology: A Review. Ind. Eng. Chem. Res. 1993, 32 (10), 2208. (4) Ghosh, T. K.; Lin, H.-D.; Hines, A. L. Hybrid AdsorptionDistillation Process for Separating Propane and Propylene. Ind. Eng. Chem. Res. 1993, 32 (10), 2390. (5) Safarik, D. J.; Eldridge, R. B. Olefin/Paraffin Separations by Reactive Absorption: A Review. Ind. Eng. Chem. Res. 1998, 37, 2571. (6) Ja¨rvelin, H.; Fair, J. R. Adsorptive Separation of PropylenePropane Mixtures. Ind. Eng. Chem. Res. 1993, 32 (10), 2201. (7) Huang, Y.-H.; Johnson, J. W.; Liapis, A. I.; Crosser, O. K. Experimental Determination of Binary Equilibrium Adsorption and Desorption of Propane-Propylene Mixtures on 13X Molecular Sieves by a Differential Sorption Bed System and Investigation of their Equilibrium Expressions. Sep. Technol. 1994, July 4, 156. (8) Yang, R. T.; Kikkinides, E. S. New Sorbents for Olefin/ Paraffin Separations by Adsorption Via π Complexation. AIChE J. 1995, 41 (3), 509. (9) Rege, S. U.; Padin, J.; Yang, R. T. Olefin/Paraffin Separations by Adsorption: π -Complaxation vs Kinetic Separation. AIChE J. 1998, 44 (4), 799.
Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999 2057 (10) Da Silva, F. A.; Macedo, M. E.; Rodrigues, A. E. Computer Aided Process Design and Optimization with Novel Separation Process; Technical Report JOU2-CT93-0337 of the DGXII European Commission, January-July, 1996. (11) Sikavitsas, V. I.; Yang, R.; Burns, M.; Langenmayr, E. Magnetically Stabilized Fluidized Bed for Gas Separations: Olefin-Paraffin Separations by π-complexation. Ind. Eng. Chem. Res. 1995, 34 (8), 2873. (12) Toth, J. State Equations of the Solid-Gas Interface Layers. Acad. Sci. Hung. 1971, 69 (3), 311. (13) Sircar, S. Role of Adsorbent Heterogeneity on Mixed Gas Adsorption. Ind. Eng. Chem. Res. 1991, 30, 1032. (14) Eic, M.; Ruthven, D. M. A New Experimental Technique for Measurement of Intracrystalline Diffusivity. Zeolites 1988, 8, 40. (15) Silva, J. A.; Rodrigues, A. E. Analysis of ZLC Technique for Diffusivity Measurements in Bidisperse Porous Adsorbent Pellets. Gas. Sep. Purif. 1996, 10 (4), 207. (16) Brandani, S.; Ruthven, D. M. Analysis of ZLC desorption curves for gaseous systems. Adsorption 1996, 2, 133. (17) Brandani, S. Analytical Solution For ZLC Desorption Curves With Bi-Porous Adsorbent Particles. Chem. Eng. Sci. 1996, 51 (12), 3283. (18) Silva, J. A.; Rodrigues, A. E. Sorption and Diffusion of n-Pentane in Pellets of 5A Zeolite. Ind. Eng. Chem. Res. 1997, 36, 493. (19) Brandani, S. Effects of nonlinear equilibrium on zero length column experiments. Chem. Eng. Sci. 1998, 53 (15), 2791.
(20) Loughlin, K. F.; Hasanain, M. A.; Abdul-Rehman, H. B. Quaternary, Ternary, Binary, and Pure Component Sorption on Zeolites. 2. Light Alkanes on Linde 5A and 13X Zeolites at Moderate to High Pressures. Ind. Eng. Chem. Res. 1990, 29 (7), 1535. (21) Costa, E.; Calleja, G.; Jimenez, A.; Pau, J. Adsorption Equilibrium of Ethylene, Propane, Propylene, Carbon Dioxide, and Their Mixtures on 13X Zeolite. J. Chem. Eng. Data 1991, 36 (2), 219. (22) Mata, V. Caracterizaca˜ o Dos Zeo´ litos 13X e 4A; Technical Internal Report of the Laboratory of Separation and Reaction Engineering (LSRE), Faculty of Engineering, University of Porto (FEUP), Porto, 1997. (23) Brandani, S.; Hufton, J.; Ruthven, D. Self-Diffusion of Propane and Propylene in 5A and 13X Zeolite Crystals Studied by the Tracer ZLC Method. Zeolites 1995, 15, 624. (24) Breck, D. W. Zeolite Molecular Sieves; John Wiley and Sons: New York, 1974. (25) Kubota, K.; Nakajima, K.; Ono, Y.; Hayashi, S. Adsorption Characteristics of Propylene on Molecular Sieve 4A. Sep. Sci. Technol. 1989, 24 (9 & 10), 709.
Received for review October 6, 1998 Revised manuscript received January 11, 1999 Accepted February 5, 1999 IE980640Z
