Ind. Eng. Chem. Res. 1990,29, 1525-1535
The nth order terms of way by (A0
X
Siexpl(f 0
fW1exp{(B,,
k m 4 are
expressed in a similar
- 8,)iiD)idMSb1exp((8, 0 - e,)iio)iaiW x ...
1525
by eq A31 from the results discussed above. This is eq 25 in the text.
(A(O)A(t,,,
=
( A ~ ( O ~ A ~ ( P+)n$3,,(2) ,i ,l
h2"
+
- 8,)iLo}idm+ exp(8,iio)Ao do1 doz ... d0,)fi. DD
Literature Cited where
exp(8,iLo)Aode1 ... de,)
P
(A30)
Here we assumed that the cross terms between wpk, u$ k, and ut play a minor role in eq A28 and are able to Le neglected. If we assume that the perturbation terms other than eq A28 in group 111, which include the perturbation factors i d # , iUm, AA, and & other than i d m @play , a minor role in the autocorrelation function of the dynamical variable, eq A6, the autocorrelation function is expressed
Harada, M.; Tanigaki, M.; Tada, Y. Law of Corresponding States of Uni-univalent Molten Salts. Ind. Eng. Chem. Fundam. 1983,22, 116-121. Janz, G. J.; Gardner, G. L.; Krebs, U.; Tonkins, R. P. T. Molten Salts: Volume 4, Part 1, Fluorides and Mixtures. Electrical Conductance, Density, Viscosity, and Surface Tension Data. J. Phys. Chem. Ref. Data 1974,3, 1-115 (fluorides and mixtures). Janz, G. J.; Tomkins, R. P. T.; Allen, C. B.; Downey, J. R., Jr.; Gardner, G. L.; Krebs, U.; Slinger, S. K. Molten Salts: Volume 4, Part 2, Chlorides and Mixtures. Electrical Conductance, Density, Viscosity, and Surface Tension Data. J. Phys. Chem. Ref. Data 1975,4,871-1178 (chlorides and mixtures). Janz, G. J.; Tomkins, R. P. T.; Allen, C. B.; Downey, J. R., Jr.; Singer, S. K. Molten Salts: Volume 4, Part 3, Bromides and Mixtures; Iodides and Mixtures. Electrical Conductance, Density, Viscosity, and Surface Tension Data. J. Phys. Chem. Ref. Data 1977, 4, 409-596 (bromides and mixtures; iodides and mixtures). Janz, G. J.; Tomkins, R. P. T.; Allen, C. B. Molten Salts: Volume 4, Part 4, Mixed Halide Melts. Electrical Conductance, Density, Viscosity, and Surface Tension Data. J. Phys. Chem. Ref. Data 1979, 8, 125-302 (mixed halides). Rice, S.A. Kinetic Theory of Ideal Ionic Melts. Trans. Faraday SOC. 1962,58, 499-510. Tada, Y.;Hiraoka, S.; Uemura, T.; Harada, M. Corresponding States Correlation of Transport Properties of Uniunivalent Molten Salts. Ind. Eng. Chem. Res. 1988,27, 1042-1049. Tosi, M. P.; Fumi, F. G. Ionic Sizes and Born Repulsive Parameters in the NaC1-type Alkali Halides-11. The Generalized HugginsMayer Form. J. Phys. Chem. Solids 1964,25,45-52. Young, R. E.; O'Connell, J. P. An Empirical Corresponding States Correlation of Densities and Transport Properties of 1-1 Alkali Metal Molten Salts. Ind. Eng. Chem. Fundam. 1971,10,418-423.
Received for review March 6 , 1989 Revised manuscript received January 2,1990 Accepted January 25, 1990
Quaternary, Ternary, Binary, and Pure Component Sorption on Zeolites. 1. Light Alkanes on Linde 5-115 Silicalite at Moderate to High Pressures H.B. Abdul-Rehman, M. A. H a s a n a i n , a n d K.F. Loughlin* King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
Pure component and multicomponent equilibrium data are reported for the adsorption of the first four n-alkanes on Linde S-115 silicalite in the temperature range 275-350 K and a t pressures up to 1.723 MPa. T h e intrinsic Henry constants and the heats of adsorption are extracted from the data by using virial isotherm techniques. The data were modeled by using five isotherms explicit in partial pressure, four simple isotherms (LRC, Toth, Mathews and Weber, Jaroniec), and one statistical thermodynamic isotherm (Ruthven). The Toth model was observed t o fit the data best for both the pure component and multicomponent data. The Toth model reduces to the Langmuir isotherm for methane and ethane except a t 275 OK for the latter. In the demethanization of natural gas, a process stream consisting of methane, ethane, propane, and n-butane
* To whom correspondence
should be addressed.
0888-5885/90/2629-1525$02.50/0
arises in which methane is generally separated from the other constituents by cryogenic distillation. Economic comparisons of cryogenic distillation with adsorption for purification involving light gases indicate that the com0 1990 American Chemical Society
1526 Ind. Eng. Chem. Res., Vol. 29, No. 7 , 1990
parison is more generally favorable to adsorption so that adsorption is commonly the preferred route even when the relative volatility is high (Ruthven, 1984). Pure component and multicomponent designs of adsorption columns are overwhelmingly dominated by the Langmuir isotherm even though this isotherm is generally not applicable to adsorption on zeolites. The objective of this paper is to model the adsorption of light alkanes on silicalite by using appropriate simple explicit isotherms in pressure, so that these models can easily be incorporated into the design of pressure swing adsorption (PSA) column processes. The prediction of binary mixtures using pure component data only is desirable and necessary to design adsorption columns adequately. In the zeolite literature, the binary models of Langmuir (Butler and Ockrent, 1930; Schay 1956; Schay et al., 1957; LeVan and Vermeulen, 1981), Langmuir-Freundlich (Sips, 1948, 1950), loading ratio correlation (Yon and Turnock, 1971), ideal adsorbed solution theory (IAST) (Myers and Prausnitz, 1965; Glessner and Myers, 1969), Ruthven’s statistical thermodynamic isotherm (Ruthven et al., 1973; Ruthven and Wong, 1985), potential theory (Bering et al., 1963), vacancy solution theory (Suwanayuen and Danner, 1980), heterogeneity models (Jaroniec, 1984),and heterogeneous ideal adsorbed solution model (HIAS) (Myers, 1987; Valenzuela et al., 1988) have been developed and applied successfully to zeolite sorption in many areas. Isotherms explicit in partial pressure, such as the Langmuir, Langmuir-Freundlich, Loading Ratio Correlation, Ruthven’s isotherm, and heterogeneity models are primarily of interest in the design of adsorption columns. Silicalite, a hydrophobic silicaeous crystalline material, is a topological type of tetrahedral framework containing five-membered rings of silicon oxygen tetrahedra. The tetrahedra form a microporous internal channel system of near-circular zigzag channels, composed of 10-membered rings, of free cross section 5.4 A cross-linked by elliptical straight channels with a major minor axis ratio of 5.75 to 5.15 A. Silicalite has a high sorption affinity for organic molecules, adsorbing molecules as large as benzene (kinetic diameter 5.8 A) but rejecting molecules larger than 6 A (e.g., neopentane 6.2 A) (Flanigan et al., 1978). Linde S-115 or silicalite is bonded with 20% clay binder to form 1/8-in.pellets. A sister material is ZSM-5, where some of the silicon is replaced by alumina. Limited adsorption studies of n-alkanes on silicalite for pure component and multicomponent equilibria, energetics of adsorption, or kinetics have elicited much information but no generally acceptable theories. The sorption of n-butane is Freundlich-like in the lower regions with exponent n = 0.92, approaching a saturation loading of 1.2 mmol/g (Lechert and Schweitzer, 1983). Ma (1984) reports a saturation loading of 1.4 mmol/g for n-hexane. Unlike 5A or 13X zeolite, silicalite does not have a well-defined cavity cell, and hence, confusion reigns over the unit cell size. Stach et al. (1984) report that the Bakaev isotherm (1966) satisfactorily models the sorption data of ethane, n-butane, n-hexane, and n-decane if different unit cell sizes of 48, 96, 96, and 192 silicon atoms per unit cell are employed. This gives maximum molecules per unit cell of 6, 8, 9, and 9, respectively, which is contrary to what would be expected if a constant unit cell size is employed. Wu and Ma (1984) assume a fixed unit cell size of 96 silicon atoms per cell, which permits a sorption loading of 7.6 molecules of n-hexane per unit cell. No model isotherm is suggested. Binary n-alkanes studies are lacking. Wang et al. (1986) reported on the binary sorption of COz and C,H, on NaZSM-5 (a neighbor to silicalite) and satisfac-
torily model their results with the vacancy solution model or Ruthven’s model using in the latter @ / u values of 0.275 for COz and 0.288 for CzH4, which is approximately equivalent to 3.6 molecules per unit cell. Klein and Abrahim (1983) have successfully applied the Langmuir mixture model to binary ethanol and water vapor. The energetics of sorption do not vary with loading except for the traditional decrease a t saturation. Values have been reported for ethane (Stach et al., 1984, Bulow et al., 1986), propane (Bulow et al., 1986), n-butane (Lechert and Schweitzer, 1983; Stach et al., 1984), and n-hexane and n-decane (Stach et al., 1984). Kinetics studies (Stach et al., 1984; Hayhurst and Paravar, 1988) reveal large differences in diffusion coefficients depending on the experimental procedure adopted.
Theoretical Section The intrinsic Henry constant relating the interaction of the sorbatesorbent system as pressure tends to zero is best evaluated by experimental measurements in this region. In the absence of experimental data at low pressure, the virial equation isotherm of Barrer and Lee (1968), C f = E exp(A,C + A,C2 + ... + AiCi + ...) (1) where f is the fugacity, C is the adsorbate concentration, K’is the Henry constant, and Ai are virial coefficients, has been found to be satisfactory. When plotted in the form In f = In -,1 + A,C + A,CZ + ... C K the plot of In (f/C) versus C becomes linear in the low concentration region, with slope A, and intercept In (l/K’). The temperature dependency of Henry’s constant is given by the van’t Hoff relationship, i.e., (3)
where K\ is the preexponential factor, -AHo is the heat of adsorption, and R is the gas constant. Plotting K’ semilogarithmicallyversus 1/T will give a linear fit of data from which the slope -AHo/R may be extracted. A t the saturation end of the isotherm, the molecules adsorbed are closely packed in a highly compressed liquidlike state. The temperature dependence of the molar volume in the adsorbed state, in the interval from the normal boiling point to the critical point, may be calculated from a linear relationship suggested by Dubinin (1960) (4)
where u* is the molar volume a t temperature T , uB is the molar volume a t boiling point TB, Tc is the critical temperature, and b is the van der Waals constant. Dubinin (1960) assumes the effective molar volume becomes independent of temperature above the critical point, whereas Ruthven and co-workers (1973) have used eq 4 above the critical temperature successfully. The theoretical saturation concentrations for Linde S-115 silicalite assuming 100% occupancy of the free voidage are given by the expression No = 0.152/~* (5) where 0.152 is derived from multiplying the voidage of the silicalite, 0.19 cm3/g of silicalite (Flanigan et al., 19781, by 0.8 to convert it to 0.152 cm3/g of pellet. The actual saturated loading (No)will be somewhat less due to steric effects.
Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 1527
GAS INLET
A
0
- CALIBRATED V O L u l E
-
ZEOLITE C U M B E R
Figure 1. Flow diagram of high-pressure multicomponent equilibrium adsorption apparatus.
Five simple isotherm models were applied to the data to determine the best fit. These were loading ratio correlation (Yon and Turnock, 1971)
where R is the loading ratio, N is the equilibrium amount sorbed, K is an equilibrium parameter analogous to the Henry constant, and n is a heterogeneity parameter Toth isotherm (Jaroniec, 1984)
isotherms all become equivalent to the Langmuir isotherm, which is also true for the Jaroniec isotherm if m = n = 1. Note that only the Toth, Mathews and Weber, and Ruthven isotherms reduce to Henry's law as p 0. All of these models are described by two or more parameters: No, the saturation concentration; K , the equilibrium parameter; n, m, heterogeneity constants; and Y, the cavity volume in silicalite. These parameters were evaluated by the Margules least-squares regression subroutine BSOLVE using the equation
-
(7) Mathews and Weber isotherm (1980)
-N --
Kf No 1 + ( K f ) " Jaroniec isotherm (1984)
where SS is the minimum sum of squares, N is the total number of data points, Cexpis the experimental concentration, and Cpreis the predicted concentration. The multicomponent form of these isotherms is available in the literature. The only one of interest for this study is the multicomponent form of the Toth isotherm given by Jaroniec (1984) as
I
where m is a heterogeneity parameter Ruthven isotherm (1971)
c=
, . I
\ - -
-,-
In this work, we found it necessary to modify this isotherm to a Langmuir-Freundlich form
I
Ni _
I ;:, I
\l/ni
(KiPi)"i
1
where C is the concentration in molecules/cavity, K' is Henry's constant in molecules/cavity/kPa, P is the molecular volume in A3, u is the cavity volume in A3, and the isotherm is subject to the restriction that m 5 u / P . However, as mentioned in the introduction, u is unclear for silicalite. The heterogeneity parameters m and n in the first four models are related to the quasi-Gaussian energy distributions. These distributions are symmetrical for m = n and assymmetrical for other sets of parameters n and m. If n > m, they show a widening to the right-hand side, whereas for n < m this widening appears on the left-hand side. For n = 1, the LRC, Toth, and Mathews and Weber
t
(13)
+ C(K;P;]",
Myers (1987) gives a different mixed gas Toth equation based on ideal adsorbed solution procedure. Experimental Section Apparatus. The apparatus (see Figure l), constructed of stainless steel, consisted of a gas recirculation loop containing an adsorbent chamber D, a mixing chamber C, a magnetic pump, a gas loading chamber B, and temperature, pressure, and composition monitoring and controlling equipment. The gas recirculation loop included empty chamber C (396.6 ccms), an adsorption cell D (whose gas volume varies depending on adsorbent quantity present: approximately
1528 Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990
575 cm3), a high-pressure (1200 psia) magnetic pump (Ruska Model 2330-802), and two manually operated valves for isolating chamber D. This chamber was located in a water bath (siphoned dry during regeneration) through which water was circulated from a thermostatically controlled water bath (Lauda Model K4R) and whose temperature was monitored with a thermocouple actuated digital indicator (Wallace and Tiernan Model 3750 K). The water bath was situated within a furnace containing four electric resistance panels that were controlled via a temperature sensor signal within the furnace by a temperature controller (Thermolyne Funatrol Model CP13315). The gas loading chamber (B, 982.47 cm3) is connected to the recirculation loop by a pressure control valve (Brooks Type 5835N) and to the gas inlet line via a dryer which was not used. Both the loading chamber (B) and adsorption cell (D) were connected to 0-200 psia differential pressure transducers (Datametrics Models 570 D-200 P-2AI-VIX) which were monitored by an electronic manometer (Datametrics Type 1014A) with three sensor switches (Datametrics Type 1049)and a null offset adapter (Datametrics Type 1056). A digital pressure gauge (Wallace and Tiernan Type 48 4349) was placed on the reference side of the differential pressure gauge attached to the loading chamber (B). The recirculation loop, loading chamber (B), and reference side of both gauges were evacuated with a WELCH DUO-SEAL vacuum pump (Type 1400) capable of an ultimate vacuum of 2 X lo4 mmHg. The composition of the gas phase was measured with a Gow-Mac chromatograph (Model 69-150) connected to a Hewlett-Packard integrater (Model 3390A). A glass chamber (A), volumetrically calibrated thrice with mercury as 250.00 cm3, was attached to chamber B initially for purposes of volumetrically calibrating the apparatus. This was removed before adsorbing gases were added. Materials. Linde S-115 silicalite, supplied by Dr. J. Sherman of Union Carbide, in the form of 1/16-in.pellets (Lot 9423840002-S-2)was the adsorbent used. Researchgrade high-purity (>99.99%) gases of methane, ethane, propane, and n-butane were purchased from Kreff Co of the U.K. Procedure. A fixed quantity of adsorbent was placed initially in a glass flask and regenerated at 375 K at the ultimate vacuum of the Edwards pump until constant weight was achieved. The entire adsorbent was transferred to the adsorption cell (D), which was then reinserted in the recirculation loop. The adsorbent was regenerated overnight under vecuum to remove any adsorbed material collected in the transfer process. To volumetrically calibrate chambers B, C, and D, helium at atmospheric pressure was expanded from chamber A into the respective evacuated chambers B, C, and D one a t a time at room temperature approximately 15 times. The mean of the resultant volumes was reported as the free volume of the vessel. After calibration, the adsorbent bed was regenerated overnight at 375 K under full vacuum. For isotherm measurement, the evacuated adsorbent cell (D) was sealed off after regeneration and cooled to the desired isotherm temperature (one of 275,300,325, or 350 K) in the water bath. Evacuated chamber B is filled with adsorbate gas to a pressure of 1.379 or 2.068 MPa, and the pressure and temperature was noted. After opening the thermostatically isolated chamber (D) to the recirculation loop, adsorbate gas is admitted from chamber B via the pressure control valve in incrementally controlled steps.
Due to release of the heat of adsorption, the system requires an hour after each step to come to thermodynamic equilibrium, a t which point the temperature and pressure of chambers B, C, and D are recorded. Using the SoaveRedlich-Kwong equation of state, for density calculations, the moles of gas in each vessel are calculated and hence the moles adsorbed computed. This is continued until either the saturation gas pressure is approached or 1.723 MPa is reached. For multicomponent mixtures, chamber D is first loaded to the desired pressure (345 or 655 kPa) with component i and isolated. Chambers B and C are then evacuated, and chamber B is loaded with another gaseous component, say j . Chamber D is opened to the recirculation loop (the pressure drops to about 230 kPa) and the magnetic pump started up. The control valve between chamber B and the recirculation loop is preset to the desired pressure (345 or 655 kPa) and is turned on to operate automatically until the pressure reattains its targeted value. This takes approximately 1 h to allow for temperature and composition equilibrium, during which time about 6 replacement gas volumes are pumped through the adsorption cell. Cell D is isolated, cell C is opened gradually to the gas chromatograph sampling valve, and its compositions measured thrice. Cell C is then evacuated and the cycle repeated with the same or other components.
Results and Discussion Pure component equilibrium adsorption data were measured for methane (up to 1.723 MPa), ethane (up to 448 kPa), propane (up to 345 kPa), and n-butane (up to 207 kPa) a t 275,300,325, and 350 K. The experimental data is reported in Table I for data base purposes. The Soave-Redlich-Kwong equation of state was used to determine the gas-phase density. Fugacities were used for all calculations involving the pure component data as pressures reached 1.723MPa but were not found necessary for the multicomponent data a t 345 or 655 kPa. The intrinsic Henry constants were extracted by using Barrer and Lee’s isotherm (typical data for ethane are shown in Figure 2) and are tabulated in Table 11. The data are plotted in the van’t Hoff form in Figure 3 and may be observed to be linear. The preexponential factor (K’J and the heat of adsorption (-AHo) were determined by regression and are tabulated in Table I1 together with literature values for -AHo for n-alkanes. Saturation concentration values were calculated with eqs 4 and 5 (physical property data were taken from Perry et al. (1963) and Maxwell (1968) assuming usage of 100% of the voidage of the zeolite). The experimental heats of sorption values reported are consistent with the reported values of Stach et al. (1984), Lechert and Schweitzer (1983), and Bulow et al. (1986). Kiselev et al. (1985) have calculated theoretical values for Kh and -AHo for these systems, and these are also reported in Table 11. As may be observed, the theoretical values of are comparable with the experimental values for ethane and propane but differ by an order of magnitude for methane and n-butane. Also, the theoretical heats of sorption are in agreement with experiment for methane and ethane but are significantly higher for propane and n-butane. The isosteric heats of sorption are plotted in Figure 4 and observed to be linear with the carbon number. Regressing the data produces the correlation -AH0 = 10.19 + 10.08n (14) where n is the carbon number. Each incremental CH2 radical increases the heat of sorption by 10.08 kJ/mol.
Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 1529 Table I. Adsorption Equilibrium Data on Linde Silicalite-115 Pellets 275
P, kPa
K
300 K
N, mmol/g
P, kPa
350 K
325 K
P, kPa
N, mmol/g
N, mmol/g
P, kPa
N, mmol/g
8.66 22.61 47.96 88.98 141.99 200.36 259.93 389.83 504.69 605.08 777.31 907.21 1086.33 1192.79 1483.95 1712.03
0.028 0.076 0.183 0.328 0.483 0.634 0.746 0.975 1.110 1.151 1.325 1.340 1.477 1.461 1.465 1.610
51.82 95.13 145.48 198.15 268.15 339.57 420.03 480.42 605.36 762.83 838.12 1059.31 1189.89 1390.12 1571.59
0.130 0.265 0.337 0.468 0.548 0.640 0.755 0.814 0.889 1.034 1.095 1.156 1.249 1.318 1.332
0.43 0.87 1.88 3.45 4.77 7.60 10.94 14.31 34.52 51.61 108.10 211.03 288.96
0.019 0.047 0.113 0.202 0.272 0.400 0.518 0.621 0.977 1.151 1.415 1.573 1.637
2.36 4.87 8.59 14.75 23.94 32.85 45.57 67.84 101.17 154.17 199.81 282.31 331.33 362.06
0.093 0.171 0.277 0.416 0.572 0.700 0.841 1.009 1.172 1.322 1.402 1.496 1.524 1.551
0.47 1.10 1.92 3.10 5.52 12.77 26.89 58.19 125.90 181.75 218.98 307.51 350.80 370.11
0.192 0.401 0.595 0.782 0.976 1.207 1.347 1.450 1.523 1.564 1.578 1.600 1.611 1.620
0.97 2.68 3.59 4.04 6.29 10.07 17.79 34.61 72.26 139.00 210.98 305.30 349.98 373.00
0.177 0.387 0.481 0.515 0.661 0.823 0.992 1.177 1.314 1.417 1.466 1.491 1.505 1.517
0.94 1.38 3.25 17.60 77.90 132.65 171.68
0.761 0.920 1.079 1.218 1.288 1.315 1.323
0.19 0.37 0.65 0.90 1.21 1.79 2.90 5.25 11.18 26.08 67.43 118.26 144.17
0.139 0.263 0.413 0.506 0.607 0.726 0.840 0.960 1.074 1.156 1.223 1.252 1.262
Methane 11.91 28.06 49.50 80.42 133.70 220.08 284.89 420.85 563.99 720.22 930.10 1112.81 1391.36 1578.20
0.227 0.495 0.715 0.951 1.181 1.450 1.575 1.803 1.877 1.962 2.062 2.040 2.069 2.141
8.03 19.97 38.97 72.06 104.08 148.94 194.57 272.15 401.96 554.47 624.52 781.45 930.79 1106.60 1212.37 1436.86 1665.77
0.068 0.168 0.307 0.502 0.649 0.934 0.956 1.133 1.352 1.509 1.528 1.606 1.732 1.718 1.808 1.819 1.903
0.23 0.58 1.25 2.30 3.41 7.89 19.82 41.53 93.63 174.80 268.89 328.60
0.165 0.353 0.620 0.874 1.043 1.358 1.596 1.732 1.864 1.957 2.027 2.055
0.85 2.77 4.33 8.11 13.24 38.17 73.11 140.45 204.73 289.99
0.179 0.473 0.626 0.891 1.099 1.442 1.594 1.733 1.792 1.838
0.65 0.98 1.65 4.29 19.22 56.95 97.35 158.85 216.91 272.89 330.67 360.59
0.920 1.106 1.288 1.470 1.598 1.674 1.702 1.720 1.732 1.750 1.769 1.784
0.19 0.39 0.58 0.87 1.52 2.87 6.77 16.66 32.05 73.04 130.70 200.86 248.97 311.64 342.36
0.252 0.477 0.603 0.778 0.974 1.143 1.301 1.412 1.481 1.522 1.556 1.570 1.569 1.577 1.590
0.14 1.19 13.40 27.44 42.61 54.55 65.68 76.15
1.145 1.276 1.368 1.397 1.419 1.436 1.459 1.482
0.05 0.10 0.23 0.42 1.11 5.45 17.84 39.48 69.57 99.73 114.98
0.356 0.656 0.878 1.016 1.142 1.251 1.301 1.339 1.362 1.378 1.386
Ethane
Propane
Butane
For the five different isotherm models, the equilibrium data were fitted to the appropriate model in either of three ways: (1) using both the theoretical No saturation concentration value and the intrinsic equilibrium parameter K value (=K’/iV,,)and optimizing the parameter n (and m if required); (ii) using either the theoretical No or intrinsic K and optimizing both the other parameter and n; (iii) optimizing all parameters, No,K,and n. For Ruthven’s
isotherm, the parameter @ / u was optimized. The results for all optimization procedures are reported in the thesis of Abdul-Rehman (1988). A very good fit was observed for the methane isotherms for all the models but the fit for most models deteriorated for higher alkanes. The Toth model was observed to fit the data best. The extra parameter m in the Jaroniec model optimized as 1,which is of course the Toth model.
1530 Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 Table 11. Intrinsic Henry Constant ( K ' ) ,Theoretical Preexponential Factor Saturation Concentration (No), (K'& and Heat of Adsorption (-AHo) for Linde 5-115 Pellets (Heats of Sorption for n-Paraffins on Silicalite from Literature Also Included)
NO,
b
0 -
0
I
o 0
A
A
component methane
ethane
0
0
propane LEGEND 275
0
300
A
325
0
.50
.90
1.20
C (MMOLES /OM
K4, mmol/g pellet/kPa
-Mo, kJ/mol
2.724 X lo4
20.39
4.714
32.78
X
1.50
1.60
300 325 350
1.895 1.860 1.826
2.4173 0.8058 0.2458
300 325 350
1.508 1.445 1.388
13.1840 4.1438 0.8058
2.908 X lo-'
39.85 40.OOc
n-butane I
.?Q
K',
mmol/g pellet/kPa 0.0210 0.0094 0.0049 0.0031 0.8058 0.2500 0.0744 0.0403
31.00O 31.0Oc
0
3
temp, mmol/g pellet K 275 3.129 300 3.022 325 2.922 350 2.828 275 2.481 300 2.399 325 2.323 350 2.251
2.10
5.493 X
48.27 51.00" 48.00* 71.00" 112.00~
PELLET)
Figure 2. Virial isotherms for ethane on Linde S-115 pellets.
n-hexane n-decane
0
1 /
*
Stach et al.. 1984. Lechert and Schweitzer. 1983. 'Bulow et al., 1986.
LEGEND METUAHE ETUANE PROPANE N-BUTANE
2.50
2.70
2.90
3.30
3.tO
I/T
3.50
3.70
0 b
0
0 1
3.90
K-Lto3)
Figure 3. van't Hoff plot for light alkanes on Linde S-115 pellets.
The optimized cage volume in the Ruthven isotherm was observed to be approximately 410 or 1800 A3, which is consistent with the Stach et al. study reported earlier. The values of the parameters employed in the Toth model to fit the data are given in Table 111, and the fit of the model to the data is presented in Figure 5. In selecting which values are optimal, the authors chose the intrinsic K value and optimized No and n route, in preference to optimizing all the parameters, the latter of course giving the minimum sum of squares. The basis for this choice is that the intrinsic K has a physical meaning, for when it is multiplied by No,the saturation concentration, Henry's constant is recovered. No detectible visual difference could be observed for either optimized procedure. The Henry's constants for the Toth equation, i.e., H = KN,, when plotted in the van't Hoff form give incorrect isoteric heats of sorption; e.g., for ethane, a value of 40 kJ/mol is obtained compared to the value of 33 kJ/mol
o o IO
CARBON
I2
14
NUMBER
Figure 4. Variation of isoteric heat of sorption with carbon number.
for the virial equation reported in Table 11. Thus, the Toth equation, which fits the high-pressure data best, doesn't do very well for Henry's constants. I t is known that the Toth equation does not have the correct analytical behavior at low pressures. Thus, it is important that, in deriving the Henry constants, isotherm equations such as the virial equation that have the correct limiting properties should be used. The optimized saturation concentrations represent 76.6%, 79.5%, a%, and 89% of the theoretical saturation concentrations based on 100% occupancy for methane, ethane, propane, and n-butane, respectively. Based on steric considerations, an 85-95'37 occupancy would be anticipated so that the results obtained are in good agreement with theory. But the fact that the largest difference occurs
Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 1531 IS
PARAMETER
TEMPERATURE
I
IN KELVIN
PARAMETER
IS
TEMFERATURE
IN
KELVIN
I-
W J J
w
a
5l \
w
J
0
f
r
2
2
tia
I2 W V
z
V 0
03
FUGACITY
$1
PARAMETER
IS
(KPA 1
TEMPERATURE I N
FUGACITY
KELVIN
91
PARAMETER
IS
TEMPERATURE
(KPA) IN
KELVIN
c w
J J W
a 5
ew
0
?-
d5 "- E 0
z
0 t-
0
?-
a fY c z
W V
0 -
?
2 0 V
?-
t
A
325
0
350 I
I
I
O16'
I
I I I I
I1 00
I
4
I
t
I I I I
I
I
1
1
1
1 0'
FUGACITY
L I t I
I
!
I
I
102
,
.d
1o3
L KPA 1
Figure 5. (a, top left) Methane, (b, top right) ethane, (c, bottom left) propane, and (d, bottom right) n-butane isotherms on Linde S-115 pellets: fit of Toth model with optimized parameters from Table 11. Table 111. Optimized Parameters of the Toth Model (Intrinsic K )for Linde 5-115 Pellets
comDonent methane
ethane
propane n-butane
NO,
temp, K
mmol/g Dellet
K, l/kPa
275.00 300.00 325.00 350.00 275.00 300.00 325.00 350.00 300.00 325.00 350.00 300.00 325.00 350.00
2.302 2.317 2.209 2.204 2.015 1.872 1.829 1.807 1.652 1.608 1.561 1.355 1.248 1.278
0.00672 0.00310 0.001 68 0.001 11 0.324 8 0.1042 0.0326 0.0179 1.275 6 0.433 2 0.1346 8.743 7 2.867 7 0.5805
n
ss
1.0000 1.0000 1.0000 1.0000 0.9046 0.9911
0.0243 0.1076 0.0749 0.0309 0.0552 0.0198 0.0088 0.0091 0.0125 0.0088 0.0096 0.0438 0.0005 0.0359
Loo00 1.oo00 0.8306 0.8344 0.9127 0.8253 0.9203 1.0000
for methane and ethane is puzzling, as steric packing would appear easier for these molecules than for the larger
molecules. This may reflect a difficulty of accurately calculating the molar volumes, especially for methane whose temperature is approximately 1.5 times its critical temperature. The heterogeneity parameter, n, appears to be temperature dependent, being 1 a t higher temperatures and decreasing a t lower temperatures. For n = 1, the Toth model reduces to the Langmuir isotherm. The fit of methane is Langmuir-like for all temperatures and ethane is Langmuir above 300 K. Binary, ternary, and quaternary multicomponent sorption data are presented in Tables IV, V, and VI. All the data were measured a t 300 K and a t 345 kPa with the exception of one methane-ethane binary mixture which was measured at 655 kPa. The binary mixtures studied were methane-ethane, methane-propane, methane-n-butane, and ethane-propane. The experimental and theoretical adsorbed-phase concentrations (using constants in Table 111)for adjacent n-alkanes are satisfactory (see methane-ethane and eth-
1532 Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 Table IV. Fit of the Multicomponent Toth Model for Binary Adsorption of Light Alkanes at 345 or 655 kPa. Theoretical Parameters from Table 111 adsorbed Dhase concn partial pressure, kPa exptl, mmol/g pellet theor, mmol/g pellet
methane 79.70 125.10 198.12 306.02 441.01 567.77 630.57 104.14 167.36 207.86 208.42 262.86 253.22 265.14 276.88 284.71 290.36
ethane 577.37 529.89 456.18 351.53 213.99 88.61 24.43 240.46 177.79 137.42 137.79 114.05 91.63 78.22 68.27 60.44 54.24
methane 0.011 0.022 0.039 0.079 0.189 0.447 0.923 0.038 0.152 0.168 0.168 0.257 0.311 0.357 0.460 0.460 0.477
ethane 1.883 1.815 1.762 1.682 1.555 1.284 0.685 1.802 1.723 1.649 1.649 1.571 1.525 1.457 1.358 1.358 1.313
methane 0.013 0.021 0.039 0.077 0.172 0.451 1.079 0.038 0.080 0.125 0.125 0.183 0.213 0.253 0.293 0.331 0.365
ethane 2.348 2.338 2.317 2.273 2.161 1.834 1.097 2.274 2.211 2.144 2.145 2.072 2.011 1.950 1.891 1.835 1.784
methane 34.47 130.80 200.30 251.24 270.84 288.19 298.72 311.12 314.29 316.82 319.90 323.65
propane 310.26 216.70 143.33 99.57 73.35 57.09 45.47 37.61 31.96 27.77 24.56 22.06
methane 0.025 0.025 0.087 0.096 0.126 0.159 0.209 0.223 0.284 0.299 0.311 0.356
propane 1.746 1.746 1.719 1.686 1.652 1.620 1.592 1.566 1.543 1.522 1.503 1.485
methane 0.002 0.012 0.025 0.042 0.057 0.074 0.092 0.110 0.126 0.141 0.156 0.171
propane 1.877 1.864 1.846 1.823 1.800 1.776 1.751 1.726 1.703 1.681 1.660 1.639
ethane 99.36 155.87 194.46 220.98 240.01 254.57
propane 244.34 187.76 150.14 123.76 104.39 89.82
ethane 0.090 0.240 0.340 0.430 0.510 0.560
propane 1.480 1.380 1.290 1.200 1.120 1.050
ethane 0.189 0.342 0.478 0.597 0.702 0.795
propane 1.694 1.547 1.419 1.309 1.214 1.130
methane 0.060 0.060 0.061 0.087 0.117 0.156 0.151 0.178 0.234 0.255
n-butane 1.392 1.392 1.375 1.358 1.343 1.330 1.318 1.307 1.298 1.289
methane 0.004 0.012 0.017 0.023 0.030 0.037 0.045 0.052 0.061 0.068
n-butane 1.501 1.492 1.486 1.479 1.471 1.463 1.454 1.446 1.436 1.428
methane 172.37 271.23 292.15 306.28 315.48 321.92 327.63 328.31 335.50 333.46
n-butane 172.37 74.42
51.76 38.32 29.12 22.75 18.48 15.33 12.96 11.27
ane-propane), but for nonadjacent components (methane-propane and methane-n-butane) the theoretical adsorbed-phase concentration of the lighter component is 200-300% too low. This suggests that an interaction parameter similar to that used by Schay et al. (1956, 1957) may be required for the lighter component for nonadjacent species. More experimental work is required to establish this concept. X-Y plots for methane-ethane, methane-propane, ethane-propane, and methane-n-butane are presented in Figures 6-9, respectively, the methane-ethane plot being at two different pressures. The agreement between theory and experiment is satisfactory. As the constant n is 1 for both species in the first plot, the theoretical curve is Langmuir and is independent of pressure. The data also appear to be independent of pressure. The ternary mixtures studied were methane-ethanepropane, methane-ethane-butane, and methane-pro-
pane-n-butane at 300 K and 345 kPa. The predicted concentrations (see Table V) using eq 14 are in good agreement with experiment with the exception that the methane predictions have a tendency to be too low. The latter also holds true for the predictions in the quaternary mixture of methaneethane-propane-n-butane (see Table VI. All the data for the ternary and quaternary mixtures are plotted as experimental concentration versus theoretical concentration in Figure 10. The model predictions using eq 14 and parameters from Table 111 may be observed to give satisfactory agreement. The use of eq 13 gave predictions that were significantly lower than actually observed.
Conclusions The sorption of light alkanes in silicalite is type I and can be modeled satisfactorily using the Toth isotherm.
Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 1533 Table V. Fit of the Multicomponent Toth Model for Ternary Adsorption of Light Alkanes a t 345 o r 655 kPa. Theoretical Parameters for Table 111 partial pressure, kPa adsorbed-phase concn exptl, mmol/g pellet theor, mmol/g pellet methane
ethane
propane
methane
ethane
propane
methane
ethane
propane
120.92 190.58 235.17 260.38 277.92 385.33 235.63
165.51 113.55 82.35 62.36 49.30 164.78 305.73
57.96 40.06 29.50 22.95 18.75 109.02 118.67
0.010 0.022 0.079 0.084 0.131 0.103 0.087
0.538 0.504 0.471 0.438 0.410 0.318 0.461
1.047 1.034 1.021 1.008 0.996 1.213 1.072
0.016 0.035 0.056 0.077 0.097 0.036 0.018
0.586 0.550 0.516 0.483 0.452 0.397 0.597
0.995 1.003 1.006 1.008 1.009 1.179 0.999
methane
ethane
n-butane
methane
ethane
n-butane
methane
ethane
n-butane
121.24 194.41 241.61 271.26 290.66 185.22 114.11 179.61 220.54
176.95 118.91 82.15 58.16 42.68 136.79 228.39 163.85 123.19
46.34 31.14 21.40 15.52 11.98 22.46 2.03 1.34 0.86
0.043 0.022 0.064 0.081 0.100 0.071 0.024 0.059 0.116
0.217 0.188 0.163 0.142 0.124 0.262 1.158 1.093 1.033
1.100 1.092 1.086 1.080 1.073 1.034 0.492 0.492 0.491
0.005 0.012 0.020 0.030 0.040 0.014 0.023 0.050 0.081
0.205 0.192 0.181 0.167 0.152 0.274 1.224 1.201 1.198
1.161 1.163 1.162 1.161 1.162 1.088 0.321 0.310 0.279
methane
propane
n-butane
n-butane
methane
propane
n-butane
130.78 90.23 61.56 43.48 31.48
109.41 73.37 48.35 33.23 23.75
methane 0.o00
propane
117.72 198.03 235.72 269.75 289.98
0.324 0.324 0.324 0.309 0.296
1.134 1.134 1.134 1.125 1.115
0.002 0.006 0.009 0.014 0.020
0.223 0.228 0.233 0.237 0.238
1.042 1.033 1.022 1.011 1.003
0.o00 0.003 0.007 0.014
Table VI. Fit of the Multicomponent Toth Model for Quaternary Adsorption of Light Alkanes a t 345 kPa. Theoretical Parameters from Table 111 adsorbed-phase concn partial pressure, kPa exptl, mmol/g pellet theor, mmol/g pellet methane ethane propane n-butane methane ethane propane n-butane methane ethane propane n-butane 123.35 202.18 245.85 274.06 292.14 183.45 112.94 68.93
109.42 71.58 48.53 33.85 24.40 117.61 185.05 230.17
62.36 41.96 29.62 21.74 16.61 23.27 23.94 22.54
0.008 0.048 0.042 0.077 0.083 0.061 0.055 0.053
49.61 31.91 21.64 15.43 11.51 19.86 22.64 23.02
0.149 0.137 0.123 0.112 0.102 0.220 0.337 0.403
0.304 0.294 0.284 0.274 0.265 0.231 0.206 0.186
1.193 1.189 1.183 1.177 1.172 1.139 1.111 1.088
0.004 0.010 0.017 0.025 0.034 0.013 0.007 0.004
0.102 0.095 0.089 0.081 0.074 0.219 0.299 0.358
0.216 0.223 0.230 0.234 0.238 0.185 0.161 0.144
0.958 0.948 0.938 0.929 0.921 0.882 0.849 0.823
w
w
2
z
a
a
T
I
/
k
I
I-
Y z
2
G
9
t
5
0
a
0:
K b.
lL v) w
W v)
a
I
LEGE: N D
a v)
1/
8 > 0
3
X
3 4 5
A
655
0
TEMPERATURE 3 0 0 K AN0 TOTAL PRESSURE 3 4 5 OR 655 K P A
25
40
.60
.80
a
v)
I
J
1.0
ADSORBED PHASE FRACTION (METHANE )
Figure 6. Binary adsorption of methane and ethane on Linde S-115 pellets: fit of multicomponent Toth model with optimized parameters from Table 11.
Intrinsic Henry constants and calculated saturated loadings are presented to enable predictions of loadings at other concentrations to be calculated. The saturation loadings occupy 75-90% of the free voidage of the silicalite. The calculated isosteric heats of sorption are consistent with literature values and increase by 10.08 kJ/mol for each
a a TEMPERATURE
>
300 K A N 0
TOTAL PRESSURE 345 KPA I
0
0 X
.20
.40
.60
ADSORBED PHASE FRACTION
,
/
.80
%
1.0
(METHANE)
Figure 7. Binary adsorption of methane and propane on Linde 54-115 pellets: f i t of mufiicomponent Toth model with optimized parameters from Table 11.
additional CH2 radical group. Calorimetric measurements of the differential heat of sorption (Stach et al., 1984) indicate that the differential heat of sorption of n-alkanes on silicalite is independent of coverage except for the traditional decrease at saturation. This implies the energetics of sorption in the cavity
1534 Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990
and ethane in the temperature range of this study. But for propane and n-butane, the Toth isotherm is applicable with n less than 1,implying energetic heterogeneity which is not observed calorimetrically. A model isotherm having energetic homogeneity needs to be developed to be consistent with all the data for this adsorbent.
-w z a
t
!!! z
0 u a a
t-
Acknowledgment
LL
The authors thank King Abdul-hiz City for Science and Technology for funding for this research project through Grant AR-6-147 and Dr. J. Sherman of Union Carbide Corporation for the samples of silicalite.
v) W
I v)
a
0
>
X
ADSORBED PHASE FRACTION
(ETHANE)
Figure 8. Binary adsorption of ethane and propane on Linde S-115 pellets: fit of multicomponent Toth model with optimized parameters from Table 11.
X
ADSORBED PHASE FRACTION
(METHANE)
Figure 9. Binary adsorption of methane and n-butane on Linde S-115 pellets: fit of multicomponent Toth model with optimized parameters from Table 11.
Nomenclature A , = coefficient for the Barrer and Lee equation b = van der Waal’s constant C = adsorbed-phase concentration, molecules/cavity o r mmol/g of pellet Ceap= experimental concentration Co = maximum attainable loading Cpre= predicted concentration from theoretical model f = fugacity, kPa K’ = Henry’s constant, molecules/cavity/kPa K = equilibrium constant, l/kPa K, = equilibrium constant for component j , l/kPa = preexponential factor for van’t Hoff relation m = parameter power or maximum number, molecules/cavity n = parameter power N = adsorbed-phase concentration, mmol/g of pellet N o = saturation concentration, mmol/g of pellet P = pressure, kPa PI = partial pressure for component j , kPa R = universal gas constant R = loading ratio SS = sum of least squares T = temperature, K T B = boiling point, K Tc = critical temperature, K X = mole fraction in adsorbed phase Y = mole fraction in gas phase Greek Symbols $ = molecular volume, A3/molecule
-ao = heat of adsorption, kJ/mol u = cage volume of uB = molar volume It*
adsorbent, A3/cavity at the boiling point, A3/molecule = molar volume at temperature T , A3/molecule
Registry No. Methane, 74-82-8; ethane, 74-84-0; propane, 74-98-6; butane, 106-97-8.
Literature Cited
LEGEND
I-
10
80
EXPERIMENTAL CONCENTRATION
(
METHANE
0
ETHANE
A
PROPANE
0
N-BUTANE
0
120
140
MMOLESIGM P E L L E T )
Figure 10. Fit of multicomponent Toth model to ternary and quaternary adsorption on Linde S-115 pellets.
are homogeneous, which is substantiated by the reduction of the Toth isotherm to the Langmuir form for methane
Abdul-Rehman, H. B. Equilibrium Adsorption of Light Alkanes and Their Mixtures at High Pressure on 5A, 13X and S-115Adsorbents. M.S. Thesis, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia 1988. Bakaev, V. A. The Statistical Thermodynamics of Adsorption in the Case of Zeolites. Dokl. Akad. Nauk. SSSR 1966,167(2),369-372. Barrer, R. M.; Lee, J. A. Hydrocarbons in Zeolite L. I1 (Entropy, Physical State and Isotherm Model). Surface Sci. 1968, 12, 354-368. Bering, B. P.;Serpinsky, V. V.; Surinova, S. I. Preliminary Computation of Adsorption Equilibrium Parameters for the AdsorbentBinary vavour Mixture System. Dokl. Akad. Nauk. SSSR 1963, i w j , 129-139. Bulow. M.: Schlodder. H.: Rees. L. V. C.: Richards. R. E. Molecular Mobility of Hydrocarbon ZSM5/Silicalite Systems Studied by Sorption Uptake and Frequency Response Methods. In New Developments in Zeolite Science and Technology, h o c . 7th Znt. Z e d . Coni., Tokyo; Murakami, Y., Iijima, A., Ward, J. W., Eds.; Elsevier: Amsterdam, 1986. Butler, J. A. V.: Ockrent., C. Studies in Electrocapillarity. Part 11. Selective Adsorption in a Solution Containing Two Active Substances. J . Phys. Chem. 1930,85, 2297-2306.
Ind. Eng. Chem. Res. 1990,29, 1535-1546 Dubinin, M. M. The Potential Theory of Adsorption of Gases and Vapours for Adsorbents with Energetically Nonuniform Surfaces. Chem. Rev. 1960,60, 235-241. Flanigan, E. M.; Bennett, J. M.; Grose, R. W.; Cohen, J. P.; Patton, R. L.; Kirchner, R. M.; Smith, J. V. Silicalite, a New Hydrophobic, Crystalline Silica Molecular Sieve. Nature 1978, 272, 512-516. Glessner, A. J.; Myers, A. L. The Sorption of Gas Mixtures in Molecular Sieves. Chem. Eng. Prog. Symp. Ser. 1969,65(96),73-79. Hayhurst, D. T.; Paravar, A. R. Diffusion of C1 to C5 normal Paraffins in Silicalite. Zeolites 1988, 8, 27-29. Jaroniec, M. Physical Adsorption on Heterogeneous Solids. In Fundamentals of Adsorption; Myers, A. L., Belfort, G., Eds.; Engineering Foundation: New York, 1984; pp 239-248. Kiselev, A. V.; Lopatkin, A. A.; Shulga, A. A. Molecular Statistical Calculations of Gas Adsorption by Silicalite. Zeolites 1985, 5, 261-267. Klein, S. M.; Abrahim, W. H. Adsorption of Ethanol and Water Vapors by Silicalite. AIChE Symp. Ser. 1983, 79(230), 53-58. Lechert, H.; Schweitzer, W. Gas Chromatographic Sorption Studies of Hydrocarbons in Pentasils with Different Si/Al Ratio. In Proc. 6th Int. Zeol. Conf.; Olsen, D., Bisio, A., Eds.; Butterworths: England, 1983. LeVan, M.; Vermeulan, T. Binary Langmuir and Freundlich Isotherms for Ideal Adsorbed Solutions. J. Phys. Chem. 1981,85,22. Ma, Y. H. Adsorption and Diffusion of Gases in Shape Selective Zeolite. In Fundamentals of Adsorption; Myers, A. L., Belfort, G., Eds.; Engineering Foundation: New York, 1984; pp 315-324. Mathews, A. P.; Weber, W. J., Jr. Mathematical Modelling of Adsorption in Multicomponent Systems. Am. Chem. SOC.,Symp. Ser. 1980, 135, 27-53. Maxwell, J. B. Data Book of Hydrocarbons; Van Nostrand: New York, 1968. Myers, A. L. Molecular Thermodynamics of Adsorption of Gas and Liquid Mixtures. In Fundamentals of Adsorption: Liapsis, A. S., Ed.; Engineering Foundation: New York, 1987; pp 3-25. Myers, A. L.; Prauznitz, J. M. Thermodynamics of Mixed Gas Adsorption. AIChE J . 1965, 11, 121-126. Perry, J. H.; Chilton, C. H.; Kirkpatrick, S. D. Chemical Engineers Handbook; McGraw-Hill: New York, 1963. Ruthven, D. M. Simple Theoretical Adsorption Isotherm for Zeolites. Nature Phys. Sci. 1971, 232, 70-72. Ruthven, D. M. Principles of Adsorption and Adsorptive Separative Processes; Wiley-Interscience: New York, 1984.
1535
Ruthven, D. M.; Loughlin, K. F.; Derrah, R. I. Sorption and Difjusion of Light Hydrocarbons and other Simple Nonpolar Molecules in Type A Zeolite; Advances in Chemistry 121; American Chemical Society: Washington, DC, 1973a; pp 330-344. Ruthven, D. M.; Loughlin, K. F.; Holborow, K. A. Multicomponent Sorption Equilibria in Molecular Sieve Zeolites. Chem. Eng. Sci. 1973b, 28, 701-709. Ruthven, D. M.; Wong, F. Generalized Stastistical Model for the Prediction of Adsorption Equilibria in Zeolites. Znd. Eng. Chem. Fundam. 1985,24, 27-32. Schay, G. J. Chem. Phys. Hung. 1956,53, 691. Schay, G. J.; Fejes, P.; Szethmary, J. Adsorption of Gas Mixtures. 1. Theory of Physical Adsorption of The Langmuir Type in Multicomponent Systems. Acta Chim. Acad. Sci., Hung. 1957,12, 299-306. Sips, J. R. On the Structure of a Catalyst Surface. J. Chem. Phys. 1948, 16, 490-495. Sips. J. R. On the Structure of a Catalyst Surface 11. J. Chem. Phvs. 1950, 18, 1024-1027. Stach, H.; Thamm, H.; Janchen, J.; Fiedler, K.; Schirmer, W. Experimental and Theoretical Investieations of the AdsorDtion of n-paraffins, n-olefins and Aromatics i n Silicalite. In Proc.'Gth Znt. Zeol. Conf.; Olsen, D., Bisio, A., Eds.; Butterworths: England, 1984; pp 225-231. Suwanayuen, S.; Danner, R. P. Vacancy Solution Theory of Adsorption from Gas Mixtures. AIChE J. 1980, 26(1), 76-83. Valenzuela, D. P.; Myers, A. L.; Talu, 0.;Zwiebel, I. Adsorption of Gas Mixtures: Effect of Energetic Heterogeneity. AZChE J. 1988, 34, 397-402. Wang, J.-G.; Chang, Y.-C.; Ma, Y. H.; Li, H.-Q.; Tong, T. D. Adsorption Equilibrium of Ethylene-Carbon Dioxide Mixtures on Zeolite ZSM-5. In New Developments in Zeolite Science and Technology: Proc. 7th Znt. Zeol. Conf., Tokyo; Murakami, Y., Iijima, A., Ward, J. W., Eds.; Elsevier: Amsterdam, 1986. Wu, P.; Ma, Y. H., The Effect of Cation on Adsorption and diffusion in ZSM-5. In Proc. 6th. Znt. Zeolitic Conf.; Olsen, D., Bisio, A., Eds.; Butterworths: England 1984; pp 253-260. Yon, C. M.; Turnock, P. H. Multicomponent Adsorption in Molecular Sieves. AIChE J . Symp. Ser. 1971, 67(117), 75-83.
Received for review October 11, 1988 Revised manuscript received July 14, 1989 Accepted August 3, 1989
Quaternary, Ternary, Binary, and Pure Component Sorption on Zeolites. 2. Light Alkanes on Linde 5A and 13X Zeolites at Moderate to High Pressures K. F. Loughlin,* M. A. Hasanain, and H. B. Abdul-Rehman King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
Pure component and multicomponent equilibrium adsorption data are reported for the adsorption of the light n-alkanes on Linde 5A and 13X pellets in the temperature range 275-350 K and at pressures up to 1.732 MPa but primarily a t a pressure of 345 kPa. The intrinsic Henry constants and heats of adsorption are extracted from the data using virial isotherm techniques. T h e experimental KOvalues for 13X are in excellent agreement with theoretical quantum mechanical calculations. For zeolite 5A, predictions of theoretical pure component, binary, and ternary profiles employing the Ruthven isotherm using intrinsic Henry constants are satisfactory. For 13X zeolite, profile predictions using the Ruthven isotherm require that the intrinsic Henry constant be increased by on average 212% to adequately fit the data. This increase is attributed to the increase in the heat of sorption with loading for these systems.
As mentioned in the previous paper in this issue (Abdul-Rehman et al., 1990), the objective of this study is to select from the published models a reliable, simple iso-
* To whom correspondence should be addressed. 0888-5885/90/2629-1535$02.50/0
therm explicit in pressure that can be incorporated in the column design of pressure swing adsorption units for the demethanization of a natural gas stream consisting of methane, ethane, propane, and n-butane. The previous paper was concerned with pure component and multi0 1990 American Chemical Society
