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Adsorption and Diffusion Parameters of Methane and Nitrogen on Microwave-Synthesized ETS-4 ´ gueda, and Alicia Garcı´a-Sanz Jose´ A. Delgado,* Marı´a A. Uguina, Vicente I. A Department of Chemical Engineering, UniVersidad Complutense de Madrid, 28040, Madrid, Spain ReceiVed December 3, 2007. ReVised Manuscript ReceiVed February 26, 2008 ETS-4 is a titanium silicate developed by Engelhard Corporation, which possesses a small pore network, the size of which can be reduced by heat treatment to improve its kinetic selectivity in nitrogen/methane separation. Most of the reported studies about ETS-4 employ crystals synthesized with conventional heating. Furthermore, information available on the adsorption properties of ETS-4, especially the diffusion properties, is scarce. In this work, Na-ETS-4 crystals have been synthesized by microwave heating and have been exchanged with strontium to obtain Sr-ETS-4 using also microwave heating. This method for obtaining the strontium form of ETS-4 has not been reported before. Both materials have been dehydrated to reduce their pore size. The adsorption and diffusion parameters of nitrogen and methane on these materials, which have not been measured for microwave-synthesized ETS-4 up to the present date, have been estimated by modeling the desorption breakthrough curves of both gases using a fixed bed of ETS-4 crystals. The kinetic selectivity of nitrogen over methane at 298 K of microwave-synthesized Sr-ETS-4 is 26. This value is higher than the maxima reported in the literature for this material.
1. Introduction The separation of nitrogen from methane is becoming increasingly important in the natural gas industry for natural gas recovery and enhanced oil recovery. Natural gases that contain significant amounts of nitrogen need to be upgraded in order to meet the pipeline quality for minimum heating value specifications (typically 10%). The removal of nitrogen from the natural gas stream is currently carried out by cryogenic distillation, which is not always economical. Despite the advantages of using adsorption for methane upgrading, this separation has been found particularly difficult because a satisfactory adsorbent has not been found yet.3 A desirable attribute in the adsorbent used for this application is high nitrogen/methane selectivity, because in this case it is easier to recover methane with high purity from methane/nitrogen mixtures in a PSA process. Separation by PSA (pressure swing adsorption) can be based either on the different adsorption affinity of the components (equilibrium separation) or on the different diffusion rates in the adsorbent (kinetic separation).4,5 For a kinetic separation of nitrogen/methane mixtures, the size of the adsorbent pores must be similar to the kinetic diameters of nitrogen (0.364 nm) and methane (0.38 nm).6 4A zeolite7,8 and carbon molecular sieves9 have been studied for the separation of methane and nitrogen, * Corresponding author. Phone: +34 91 3944119; Fax: +34 91 3944114. E-mail address:
[email protected]. (1) Jayaraman, A.; Herna´ndez-Maldonado, A. J.; Yang, R. T.; Chinn, D.; Munson, C. L.; Mohr, D. H. Chem. Eng. Sci. 2004, 59, 2407. (2) Engelhard Corporation, Adsorption Processes for Natural Gas Treatment, A Technology Update, www.engelhard.com, 2005. (3) Yang, R. T. Adsorbents: Fundamentals and Applications; Wiley: New Jersey, 2003. (4) Ruthven, D. M.; Farooq, S.; Knaebel, K. S. Pressure Swing Adsorption; VCH: New York, 1994. (5) Yang, R. T. Gas Separation by Adsorption Processes; Imperial College Press: Singapore, 1997. (6) Breck, D. W. Zeolite Molecular SieVes: Structure, Chemistry and Use; Wiley: New York, 1974. (7) Habgood, H. W. US Patent 2,843,219, 1958. (8) Habgood, H. W. Can. J. Chem. 1958, 36, 1384. (9) Ackley, M. W.; Yang, R. T. AIChE J. 1990, 36, 1229.
because their pore size fulfills this condition. However, the process with 4A zeolite was limited to low temperatures (-79 to 0 °C) and high methane feed content (g90%). Cavenati et al.10 have studied the separation of the mixture CH4/CO2/N2 by layered PSA using zeolite 13X and carbon molecular sieve 3K as adsorbents, obtaining methane with a purity of 89%. The interest of the nitrogen/methane separation has prompted the search of new adsorbents, among which ion-exchanged clinoptilolites and ETS-4 are the most promising ones.1 As clinoptilolites are natural zeolites, and the synthetic form is difficult to prepare,11 its use is hindered by the variability in the extra-framework cation composition with the extraction mine. ETS-4 is a synthetic material, and therefore its adsorption properties can be controlled more easily. ETS-4 is a titanium silicate developed by Engelhard Corporation, which possesses a small pore network, the size of which can be reduced by heat treatment to improve its kinetic selectivity.12–14 The shrinkage in ETS-4 is a direct consequence of structural water loss during the heat treatment, producing deformation of the titania chains in this material and loss of crystallinity.14 Although the crystalline structure of as-synthesized ETS-4 (Na-ETS-4) collapses at temperatures near 200 °C, the thermal stability can be improved by ion-exchanging Na with alkaline arth cations, preferably Sr and Ca.13 Intensive research has been performed on the synthesis and structural characterization of ETS-4 in the literature.15–20 Most of the reported studies about (10) Cavenati, S.; Grande, C. A.; Rodrigues, A. E. Chem. Eng. Sci. 2006, 61, 3893. (11) Williams, C. D. Chem. Commun. 1997, 2113. (12) Kuznicki, S. M. US Patent 4,938,939, 1990. (13) Kuznicki, S. M.; Bell, V. A.; Petrovic, I.; Desai, B. T. US Patent 6,068,682, 2000. (14) Kuznicki, S. M.; Bell, V. A.; Nair, S.; Hillhouse, H. W.; Jacubinas, R. M.; Braunbarth, C. M.; Toby, B. H.; Tsapatsis, M. Nature 2001, 412, 720. (15) Philippou, A.; Anderson, M. W. Zeolites 1996, 16, 98. (16) Mintova, S.; Valtchev, V.; Angelova, S.; Konstantinov, L. Zeolites 1997, 18, 269. (17) Nair, S.; Jeong, H. K.; Chandrasekaran, A.; Braunbarth, C. M.; Tsapatsis, M.; Kuznicki, S. M. Chem. Mater. 2001, 13, 4247. (18) Nair, S.; Tsapatsis, M.; Toby, B. H.; Kuznicki, S. M. J. Am. Chem. Soc. 2001, 123, 12781. (19) Warzywoda, J.; Yilmaz, B.; Miraglia, P. Q.; Sacco, A., Jr. Microporous Mesoporous Mater. 2004, 71, 177. (20) Pavel, C. C.; Vuono, D.; Catanzaro, L.; De Luca, P.; Bilba, N.; Nastro, A.; Nagy, J. B. Microporous Mesoporous Mater. 2002, 56, 227.
10.1021/la7037894 CCC: $40.75 2008 American Chemical Society Published on Web 05/17/2008
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ETS-4 employ crystals synthesized with conventional heating, that is to say, introducing the autoclave containing the precursor components in a conventional furnace to induce the crystallization. The transformation into Sr-ETS-4 by ion exchange is also usually carried out at high temperature (80-180 °C) with conventional heating. Recently, Coutinho et al.21 have developed a method to synthesize ETS-4 crystals using microwave heating, which allows considerable reduction of the synthesis time. This method results in volumetric heating that produces fast nucleation and growth as well as fast supersaturation of the mixture, which leads to shorter reaction times. Additionally, microwave radiation enables the suppression of undesired phases compared with conventional heating.22 On the other hand, the information available about the adsorption properties of ETS-4, and especially the diffusion properties, is scarce. Jayaraman et al.1 have reported the adsorption isotherms and the diffusion time constants of nitrogen and methane in Sr-ETS-4. Conventional synthesis was used in this work. Marathe et al.23,24 have studied the adsorption equilibrium and kinetics of nitrogen and methane on Na-ETS-4 and Sr-ETS-4 in the form of pellets with a volumetric method, taking into account the effect of the dehydration temperature, and they have obtained the corresponding adsorption and diffusion parameters. Both the synthesis and the ion-exchange step in these works were carried out with conventional heating. In this work, Na-ETS-4 crystals have been synthesized by microwave heating and have been exchanged with strontium to obtain Sr-ETS-4 also using microwave heating. Both materials have been dehydrated to reduce their pore size. The adsorption and diffusion parameters of nitrogen and methane on these materials, which have not been measured for microwavesynthesized ETS-4 currently, have been estimated by modeling the desorption breakthrough curves of both gases using a fixed bed of ETS-4 crystals.
2. Experimental Section Synthesis and Characterization of Na-ETS-4 and Sr-ETS-4. Na-ETS-4 was synthesized following the method proposed by Coutinho et al.21 This method uses silica gel as the source of silicon and the following composition of the precursor gel: 8.5 H2O2/TiO2/ 10 SiO2/16 NaOH/761 H2O. The synthesis procedure is explained here because details not reported in their reference are included. Two different solutions are prepared: the first one contains NaOH (SDS, 98%) dissolved in deionized water, to which the silica gel (Merck) dissolved in water is added slowly; and the second solution is also composed of NaOH dissolved in water, to which the source of titanium (titanium butoxide, Alfa Aesar, 99%) is added dropwise. Hydrogen peroxide (Panreac, 33% v/v) is added rapidly to the second solution to dissolve the white precipitate formed. Finally, the two solutions are mixed together with the amount of water necessary to maintain the molar composition, pouring the solution with titanium over the one with silicon. The mixed solution is stirred until turbidity disappears. The precursor gel is put in a Teflon reaction vessel of 250 mL, and heated at 200 °C in a microwave oven (MLS-1200 MEGA) for 10 h. After this crystallization time, the solid is filtered and washed with deionized water until neutral pH is obtained. Afterward, it is dried at 70 °C overnight. Sr-ETS-4 was obtained by mixing Na-ETS-4 crystals with SrCl2 · 6H2O 1 M (25 mL per gram of solid) in a microwave reactor of 70 mL at 200 °C for 1 h. Afterward, the crystals are washed with deionized water, until the presence of (21) Coutinho, D.; Losilla, J. A.; Balkus, K. J., Jr. Microporous Mesoporous Mater. 2006, 90, 229. (22) Arafat, A.; Jansen, J. C.; Ebaid, A. R.; van Bekkum, H. Zeolites 1993, 13, 162. (23) Marathe, R. P.; Mantri, K.; Srinivasan, M. P.; Farooq, S. Ind. Chem. Eng. Res. 2004, 43, 5281. (24) Marathe, R. P.; Farooq, S.; Srinivasan, M. P. Langmuir 2005, 21, 4532.
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Figure 1. Scheme of the setup for the fixed-bed adsorption experiments. Table 1. Conditions and Model Parameters for Estimating Void Volume and Dispersion Coefficient with a Bed of Glass Beads particle radius bed length bed porosity bed diameter feed composition pressure at bed outlet purge flow rate methane-helium diffusivity temperature
rp ) 0.0005 m Lglass ) 0.15 m glass ) 0.4 di ) 0.009 m 10% CH4/90% He P0 ) 95078 Pa Q ) 1.31 · 10-6 m3 s-1 Dm ) 6.81 · 10-5 m2 s-1 T ) 298 K
Cl- is not detectable with AgNO3 (1%). An ion-exchange degree of 93% was achieved with this method. The crystalline structure and degree of crystallinity of the synthesized materials at different temperatures were analyzed by XRD (Phillips, D5000 model, Cu KR radiation, Ni filter), equipped with a high-temperature chamber, and its composition was determined by XRF (Phillips, AXIOS model). The morphology and the size of crystals were determined by SEM (JEOL, JSM-6400 model). Adsorption Experiments. All the gases used in this work had purity higher than 99.5%, supplied by Praxair. A scheme of the experimental setup used to carry out the adsorption experiments is shown in Figure 1. The flow of each gas was controlled with mass flow controllers (Brooks). The stainless steel column (i.d. ) 9 mm, 25 cm long) containing the adsorbent bed is surrounded by two stainless steel spiral tubes (1/8 in), one of them to preheat the feed gas (shown separately for simplicity in Figure 1), and the other (not
Figure 2. Plot of mass spectrometer signal vs time for a complete adsorption–desorption experiment (run 8, Table 2).
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Table 2. Experimental Conditions for Desorption Breakthrough Experiments with Methane and Nitrogen Diluted in Helium and Estimated Adsorption Parameters run
gas
adsorbent
outlet P(104 Pa)
y0
1 2 3 4 5 6 7 8 9 10
CH4 CH4 N2 N2 N2 CH4 CH4 N2 N2 N2
Na-ETS-4 Na-ETS-4 Na-ETS-4 Na-ETS-4 Na-ETS-4 Sr-ETS-4 Sr-ETS-4 Sr-ETS-4 Sr-ETS-4 Sr-ETS-4
9.42 9.46 9.47 9.34 9.44 9.42 9.51 9.53 9.48 9.51
0.192 0.100 0.056 0.138 0.147 0.184 0.229 0.077 0.150 0.119
QHe at 293 K (10-6 m3 s-1) T (K) KH (mol kg-1 Pa-1) Dc/rc2 (s-1) -∆H (kJ mol-1) Ediff (kJ mol-1) 1.21 1.35 1.46 1.35 1.29 1.21 1.34 1.32 1.34 1.36
3.12 · 10-6 1.14 · 10-6 2.04 · 10-6 1.59 · 10-6 1.09 · 10-6 9.50 · 10-7 7.60 · 10-7 5.32 · 10-6 4.09 · 10-6 3.00 · 10-6
298 318 298 308 318 298 318 298 308 318
shown) to control the bed temperature with a thermostated water bath. The column and the surrounding spiral tubes are covered by an electrical coaxial furnace, so that the bed temperature can be controlled between 25 and 600 °C. The bed temperature is measured by a thermocouple in contact with the adsorbent, and the pressure at the bed inlet is measured with a manometer. A glass hollow stick (i.d. ) 2 mm, o.d. ) 8 mm, 10 cm long) reduces the dead volume before the bed, through which the thermocouple (o.d. ) 1.5 mm) is inserted, and the dead volume after the bed is reduced with glass beads (1 mm diameter). Small layers of glass wool are placed between the three column sections (glass stick-adsorbent-glass beads). All the connections are made of Teflon and stainless-steel tubing (1/8 in). Adsorptionexperimentswereperformedbypassingnitrogen-helium and methane-helium mixtures through the column containing 1 g of adsorbent (Na-ETS-4 or Sr-ETS-4) and purging with helium to obtain the desorption breakthrough curves. Before the adsorption experiments, Na-ETS-4 and Sr-ETS-4 were dehydrated once in situ for 12 h in helium flow at 150 and 200 °C, respectively, taking into account the XRD characterization results, discussed below. A mass spectrometer (Pfeiffer Vacuum, Thermostar model) was employed for monitoring the nitrogen and methane concentrations at the column exit. The gas flow rate at the bed exit was measured with a bubble meter. An example of the experimental breakthrough curve obtained for a complete adsorption–desorption experiment (run 8 in Table 2) is shown in Figure 2. The start of the adsorption and desorption experiments correspond to the simultaneous turn of valves V-1 and V-2 in Figure 1, so that the feed gas (methane-helium mixture or pure helium) which was bypassing the bed, starts to pass through it. Only the desorption curves were employed to estimate the adsorption and diffusion parameters, and not the adsorption ones, because the signal noise at the high concentration level corresponding to the end of the adsorption experiment is quite important, whereas it is almost nonexistent at the low concentration level (Figure 2). This noise increases the error in the calculation of the area above the adsorption curve, which affects the calculation of the adsorbed amount. Micropore diffusion is dominant at the end of both adsorption and desorption experiments, so the error in the estimation of the micropore diffusivity is also higher if the adsorption curve is employed. Another well-known experimental technique to estimate adsorption and diffusion parameters, the ZLC method,25,26 only uses the desorption curve for this purpose. As is shown in Figure 2, the sharp change in the MS signal when the valves are turned allows determination of the zero time point of the desorption curve accurately. To take into account the delay time caused by the void volume outside the bed and the glass beads section, this time (calculated as dead volume/purge volumetric flow) was substracted from the experimental time previously determined. The calculation of the void volume is explained in section 4.2. To convert the MS signal to dimensionless concentration values (c/c0), the baseline was substracted from the desorption curve, and the resulting data were divided into their maximum value (the initial ones). (25) Eic, M.; Ruthven, D. M. Zeolites 1988, 8, 40. (26) Soares, J. L.; Moreira, R. F. P. M.; Jose´; H. J.; Grande, C. A.; Rodrigues, A. E. Sep. Sci. Technol. 2004, 39, 1989.
4.0 · 10-3 6.0 · 10-3 5.0 · 10-2 6.0 · 10-2 6.0 · 10-2 3.2 · 10-4 6.0 · 10-4 7.0 · 10-3 9.0 · 10-3 1.3 · 10-2
39 39 25 25 25 8.6 8.6 22 22 22
16 16 7 7 7 21 21 24 24 24
It must be noted that the open flow method used in this work, like the ZLC method, does not provide independent equilibrium measurements, since both equilibrium and kinetic parameters are extracted from the kinetic curves. Other techniques, such as the volumetric and gravimetric methods, can give independent equilibrium measurements. However, the volumetric methods require a large amount of sample to obtain reliable data, and the gravimetric methods require an accurate correction of the buoyancy effect, especially for small changes of weight (the average weight change is 0.06% in the experiments carried out in this work, while being of only 0.03% for methane in Sr-ETS-4), which is difficult for most commercially available gravimetric instruments (thermogravimetric devices). The open flow method used in this work was chosen for its simplicity and because a small amount of sample is required (1 g). The use of this kind of technique to obtain adsorption equilibrium data is well-documented in the literature.27–29
3. Model Description The model used to describe the dynamics of the adsorbent fixed bed is derived from the mass, energy, and momentum balances, including the following assumptions: (i) The flow pattern is described with the axially dispersed plug flow model. (ii) Local thermal equilibrium is assumed between the gas and the adsorbent particles. (iii) The mass transfer rate is represented by a linear driving force (LDF) model. (iv) The gas phase behaves as an ideal gas mixture. (v) Radial concentration and temperature gradients are negligible. The partial differential equations and the corresponding boundary conditions of this model have been described in previous work.28 This model is based on the one proposed by Da Silva and Rodrigues,30 introducing several simplifications to reduce the computational time: a lumped mass transfer coefficient is used and local thermal equilibrium is assumed. However, this model had to be improved so as to take into account the dispersion caused by the void volume filled with glass beads (Figure 1), as the length of this zone is significantly larger than the bed length (13 cm vs 1.7 cm approx.). Since there is no adsorption and the pressure drop is negligible in the glass beads zone, the corresponding dynamics can be described with the mass balance for the adsorptive gas only, in a simplified form: (27) Harlick, P. J. E.; Tezel, F. H. Microporous Mesoporous Mater. 2004, 76, 71. (28) Delgado, J. A.; Uguina, M. A.; Sotelo, J. L.; Ruiz, B.; Go´mez, J. M. Adsorption 2006, 12, 5. (29) Belmabkhout, Y.; Pirngruber, G.; Jolimaitre, E.; Methivier, A. Adsorption 2007, 13, 341. (30) Da Silva, F.; Rodrigues, A. E. AIChE J. 2001, 47, 341.
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∂yglass DL,glass ∂2yglass u(t) ∂yglass + ) 2 2 ∂t L ∂x glassLglass ∂x
(1)
glass
where yglass is the mole fraction of the adsorptive gas (nitrogen or methane), t is time, DL,glass is the axial dispersion coefficient in the glass beads zone, glass and Lglass are its porosity and its length, respectively. The second term in this equation is positive because, unlike the bed zone, the flux going from x ) 1 to x ) 0 is considered positive. The variable u(t) is the superficial velocity of the gas coming out of the bed, which may change with time. The boundary conditions for this equation are:
x)1
yglass ) ybed
x)0
dyglass )0 dx
(2)
The boundary condition at x ) 1 equates the mole fraction of the adsorptive gas at the bed exit and the inlet of the glass beads zone. Note that ybed and yglass are different variables in the model. In order to equate the fluxes of this gas, the boundary condition at the bed exit must be changed from dybed/dx ) 0 to
x)1-
( )
( )
DL,bed DL,glass dybed dyglass bed ) glass Lbed dx Lglass dx
(3)
The complete model was solved numerically using the PDECOL program31 (FORTRAN version of 1978), which uses orthogonal collocation on the finite elements technique. Further information about the calculation and fitting procedures used in this work can be found elsewhere.32
4. Results and Discussion 4.1. ETS-4 Characterization. The SEM images in Figure 3 show the crystals of Na-ETS-4 synthesized with microwave heating. These crystals are composed of aggregated thin platelike crystallites (∼0.3 µm thick, ∼5 µm long) that form spherulites, with morphology similar to that of ETS-4 synthesized in other works.19,21 Some single spherulites, with a size of about 40 µm, are observed. However, many of them are intertwined, so that it is difficult to estimate the average particle size. A significant presence of crystal defects caused by intergrowth is also observed, which is typical of ETS-4 materials.33,34 The final product composition as estimated by XRF was the following (% w/w): Ti ) 21.204, Si ) 22.803, O ) 44.980, Na ) 10.96, others ) 0.053. Figure 4 shows the XRD patterns measured at different dehydration temperatures of Na-ETS-4 and Sr-ETS-4 synthesized with microwave heating. The patterns of Na-ETS-4 match well with the ones reported by Coutinho et al.21 and Marathe et al.23 The pattern of Sr-ETS-4 at low temperatures (from 30 to 100 °C) resembles very much the one given by Braunbarth et al.35 for Sr-ETS-4 without heat treatment. The displacement of the peaks to higher angles with heat treatment for Sr-ETS-4 indicates a reduction in pore size according to Bragg’s law. It is observed that both materials lose their characteristic structures at high temperatures, but the thermal stability of Sr-ETS-4 is higher, keeping a high level of crystallinity up to 200 °C, whereas the (31) Madsen, N. K.; Sincovec, R. F. ACM Trans. Math. Soft. 1979, 5, 326. (32) Delgado, J. A.; Nijhuis, T. A.; Kapteijn, F.; Moulijn, J. A. Chem. Eng. Sci. 2002, 57, 1835. (33) Miraglia, P. Q.; Yilmaz, B.; Warzywoda, J.; Bazzana, S.; Sacco, A., Jr. Microporous Mesoporous Mater. 2004, 69, 71. (34) Miraglia, P. Q.; Yilmaz, B.; Warzywoda, J.; Bazzana, S.; Sacco, A., Jr. J. Cryst. Growth 2004, 270, 674. (35) Braunbarth, C.; Hillhouse, H. W.; Nair, S.; Tsapatsis, M.; Burton, A.; Lobo, R. F.; Jacubinas, R. M.; Kuznicki, S. M Chem. Mater. 2000, 12, 1857.
Figure 3. SEM images of Na-ETS-4 synthesized in this work.
Na-ETS-4 structure is kept up to 150 °C only. In view of these results, Na-ETS-4 and Sr-ETS-4 were dehydrated at 150 and 200 °C for the adsorption experiments, respectively. 4.2. Modeling of the Effect of Void Volume on the Desorption Breakthrough Curves. In order to estimate the adsorption and diffusion parameters by modeling the experimental desorption breakthrough curves, it is essential to describe adequately the effect of void volume in the installation. To do
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Figure 5. Desorption breakthrough curve of a methane/helium mixture with a bed a glass beads. Conditions are given in Table 1. Continuous line is obtained with the model.
Figure 4. XRD patters of ETS-4 for different dehydration temperatures. (a) Na-ETS-4. (b) Sr-ETS-4.
so, an experiment was performed feeding a methane/helium mixture to the column filled with glass beads (together with the glass hollow stick) and purging with helium afterward. The experimental desorption curve was fitted with the proposed model, leaving as adjustable parameters the void volume outside the bed of glass beads and the dispersion coefficient in this zone. The void volume inside the bed is considered with the porosity, glass. The following correlation was proposed to estimate the axial dispersion coefficient36
DL )
Dm (E + 0 . 5ScRe) glass 0
(4)
where Dm the molecular diffusivity for the binary mixture, Sc is the Schmidt number, Re is the particle Reynolds number, and E0 is the stagnant contribution to axial dispersion. Assuming plug flow in the void volume outside the bed (it is composed of 1/8 in tubes and the glass hollow stick, which leaves a narrow passage for the gas, 0.5 mm wide), its effect is considered by subtracting a delay time (void volume/purge volumetric flow) from the experimental desorption curve, which starts at the moment that helium is connected to the column by V-1 (Figure 1). Conditions and model parameters are given in Table 1. The void volume and E0 were estimated as 8.7 · 10-6 m3 and 3, respectively. A comparison between the experimental and the predicted breakthrough curves is shown in Figure 5, where it is observed that the model reproduces the experimental data very well. These parameters were fixed to the estimated values for the rest of simulations. 4.3. Estimation of the Adsorption and Diffusion Parameters. A set of desorption breakthrough experiments was carried out to study the adsorption properties of methane and nitrogen on (36) Wakao, N.; Kagei, S.; Nagai, H. Chem. Eng. Sci. 1978, 33, 183.
Figure 6. Desorption breakthrough curves of methane/helium and nitrogen/helium mixtures using beds of Na-ETS-4 and Sr-ETS-4. Conditions are given in Table 2. Lines are the theoretical curves. (a) Methane/Na-ETS-4 system: squares, run 1; circles, run 2. Thin continuous lines, LDF model with Ω(t). Dashed line, LDF model with Ω ) 15. (b) Nitrogen/Na-ETS-4 system: squares, run 3; circles, run 4; triangles, run, 5. Dashed line in the graph on the right was obtained assuming that N2 is distributed among two different adsorption sites with different diffusivity (see text). (c) Methane/Sr-ETS-4 system: squares, run 6; circles, run 7. (d) Nitrogen/Sr-ETS-4 system: squares, run 8; circles, run 9; triangles, run 10.
the synthesized materials. Figure 6 shows the results obtained, and the conditions are given in Table 2. The experimental curves were fitted with the model described previously, and the model parameters are given in Table 3. The axial dispersion coefficient in the bed of crystals was estimated with an expression available in the literature for beds of small particles (
