Adsorption and Diffusion of Methane and Nitrogen in Barium

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Adsorption and Diffusion of Methane and Nitrogen in Barium Exchanged ETS-4 B. Majumdar, S. J. Bhadra, R. P. Marathe, and S. Farooq* Department of Chemical and Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore 117576 ABSTRACT: Single component equilibrium and uptake of methane and nitrogen in barium exchanged ETS-4, Ba-ETS-4, have been measured in a constant volume apparatus over a wide range of temperatures and pressures followed by binary measurements in a differential adsorption bed at some selected conditions. Similar binary data in two strontium exchanged samples have also been included for which unary data were earlier reported from our laboratory.12 Adsorbent particles used in these measurements were obtained by pressure-binding very fine crystals of Ba-ETS-4 synthesized in this laboratory, thus giving rise to a bidispersed pore structure with the controlling resistance to diffusion in the micropores. The effect of dehydration temperature on equilibrium and kinetics of aforementioned gases in Ba-ETS-4 has also been investigated. The uncoupled kinetic selectivity of nitrogen over methane in Ba-ETS-4 measured in this study far exceeds the selectivity reported for methane-nitrogen separation in other adsorbents in the literature. Kinetic selectivity including the coupling of equilibrium isotherm and uptake has also been calculated from binary measurements and is found to be equally encouraging. The impact of isotherm models on the concentration dependence of micropore diffusivity has been analyzed on the basis of chemical potential gradient as the driving force for diffusion. Binary equilibrium and kinetic models based on parameters independently established from unary experiments have been proposed that are able to explain the transport mechanism and capture the essential features of measured binary data.

’ INTRODUCTION Titanium silicate molecular sieves are a new class of materials, which provide uniform pore size like alumino-silicate zeolites. Over the last 15 years, Engelhard Corp. has developed and patented a family of titanium silicate (aNa2O:bTiO2:ySiO2:zH2O) molecular sieves and has named them ETS-4, ETS-10, and ETS-14.1-3 Small pore ETS-4 is structurally more interesting. It has a distinct octahedral-tetrahedral structure, which is faulted in the [100] and [001] directions.4 In other words, the 12-membered ring (12MR) is always blocked and is therefore inaccessible to diffusing molecules. This faulting, however, does not block the 8-ring pores (8MR). Thus, the channels formed by the 8MR are the sole channels for transport of diffusing molecules. Improved separation by cation exchange is well-known in conventional alumino-silicate zeolites.5 Lithium exchanged 13X zeolite used in the vacuum swing air separation cycle licensed by Praxair is one such example. Similar improvement has also been reported for ETS-4 in the patent literature and was confirmed in a recent publication from our laboratory.6 Significant kinetic differentiation between nitrogen and methane upon exchanging the as- synthesized sodium form of ETS-4 with bivalent strontium cation is evident from Table 1 extracted from the aforementioned publication. The uniqueness of ion exchanged variants of ETS-4 is the contraction of its 8MR channels at a molecular scale with increasing dehydration temperature,7 which makes it a potential adsorbent material for the separation of gas molecules of similar size. Methane-nitrogen separation for natural gas upgrading is one leading example of industrial importance that can benefit from the exploitation of the aforementioned transport channel contraction in ETS-4. Olefin-paraffin separation (ethylene from r 2011 American Chemical Society

ethane, propylene from propane, etc), which is currently the most energy intensive distillation process in the petrochemical industry requiring low temperature, high pressure, and over 100 trays, is another potential area where a custom designed ETS-4 can significantly impact the economics. In fact, the unique pore contraction property of ion exchanged variants of ETS-4 opens up practically unlimited opportunities in gas separation. Surprisingly, adsorption and diffusion of gases in this class of materials, which are vital for fully exploiting its vast potential in adsorption gas separation, has not received much attention in the open literature. Most of the studies on ETS-4 published in the open literature have mainly focused on its synthesis and crystallization kinetics from various precursors.8-10 Structural elucidation is another focus area of published studies on ETS-4. In Table 1, also included is a summary of the impact of increasing dehydration temperature on the equilibrium and transport of methane and nitrogen in strontium exchanged ETS-4, Sr-ETS-4. Decreasing uptake rate with increasing dehydration temperature provided direct evidence of pore contraction, also shown by Nair et al.11 from powder neutron diffraction and vibrational spectroscopy. It is important to note that methane has a higher polarizability than does nitrogen. Hence, like in all known adsorbents, methane initially showed stronger adsorption than nitrogen in strontium exchanged ETS-4 sample. Pore contraction also decreased the pore potential for adsorption of the gas molecules, but the drop was greater for (the marginally bigger) methane and eventually led to a reversal in adsorption affinity. It is clear that the kinetic Received: July 2, 2010 Accepted: December 7, 2010 Revised: November 26, 2010 Published: January 25, 2011 3021

dx.doi.org/10.1021/ie1014124 | Ind. Eng. Chem. Res. 2011, 50, 3021–3034

Industrial & Engineering Chemistry Research

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Table 1. Effect of Dehydration Temperature on Adsorption and Diffusion of Gases in Sr-ETS-4 in the Linear Range of the Isotherm at 10 °C (Extracted from Marathe et al.13) dehydration

a

adsorbent

temperature (°C)

KN2/KCH4

(Dco,N2)/(r2c ) (10-3 s-1)

(Dco,CH4)/(r2c ) (10-3 s-1)

(Dco,N2)/(Dco,CH4)

kinetic selectivitya

Na-ETS-4 Sr-ETS-4

170 190

0.7 0.34

0.049 6.72

0.039 0.018

1.3 373

0.8 6.6

230

0.44

3.2

0.015

213

270

2.1

0.41

0.013

31.5

310

1.1

0.19

0.01

19

6.4 11.8 4.8

Kinetic selectivity = KN2/KCH4 ((Dco,N2)/(Dco,CH4))1/2.

selectivity of nitrogen over methane, defined as KN2/KCH4 ((Dco)N2/(Dco)CH4)1/2, was adversely affected by the initially stronger methane equilibrium. Hence, it was felt that an obvious direction for further improvement of this material would be to gain greater control on pore contraction to maximize the kinetic selectivity by synchronizing the optimum in equilibrium and diffusivity ratios. On the basis of the aforementioned premise, the degree of control on pore contraction gained by controlling the extent of cation exchange was examined, but it was concluded that complete exchange gave the best results.12 In search for attaining a higher selectivity, the focus was turned to barium exchanged ETS-4, Ba-ETS-4. However, in view of the findings with partial strontium exchange, we restricted our investigation to only complete barium exchanged samples. Considering the practical importance of methane-nitrogen separation, the focus was on adsorption and diffusion study of methane and nitrogen. The following advances are reported in this Article: (i) Synthesis and characterization of Ba-ETS-4. (ii) Effect of dehydrating the barium exchanged titanium silicate adsorbent at a progressively higher temperature on its (ideal) selectivity of nitrogen over methane in the linear range of the isotherm. (iii) Detailed experimentation on unary and binary equilibrium and kinetics for the sample showing maximum ideal selectivity. The binary study also included two Sr-ETS-4 samples, Sr190 and Sr270, that were shortlisted in our unary studies published earlier.6,13 190 and 270 refer to the temperature (in °C) at which the samples were dehydrated. (iv) A model is proposed that predicts the binary uptake reasonably well using single component isotherm parameters and diffusional time constants established from independent unary experiments.

’ EXPERIMENTAL SECTION Synthesis Procedure. ETS-4 is a titanium silicate containing exchangeable Naþ cation and should, by default, imply Na-ETS4. The cation can be exchanged to obtain the desirable variant. Direct synthesis of other cationic form is not known. Kuznicki2 and Chapman and Roe14 independently reported the synthesis of ETS-4 for the first time. Since then, a number of reports on synthesis and characterization of ETS-4 have been published in the open literature. The main difference among these studies is the reagents used to provide the precursors. The amount of each reagent in the initial synthesis gel also differs in these reports. In this study, an inorganic source of titanium, titanium chloride, was used in the initial synthesis gel.8 The gel composition was 4.42

Na2O:0.95 K2O:TiO2:5.71SiO2:81.88H2O. An alkaline solution was prepared by mixing 63.0 g of sodium silicate (28.6% SiO2, 8.82% Na2O, and 62.58% H2O, Merck) and 11.4 g of NaOH pellets (Merck). The mixture was stirred vigorously for 10 min. 54.4 g of titanium chloride solution made from 27.2 g of 30% TiCl3 solution in HCl (Acros Organics, Morris Plains, NJ) and 27.2 g of deionized water was then added dropwise to the alkaline solution followed by stirring for one-half an hour. The gel-like mixture assumed a black color. 9.4 g of potassium fluoride dihydrate (KF 3 2H2O, Nacalai Tesque Inc., Kyoto, Japan) was added to the blackish gel as a solubilizing agent, and the mixture was stirred for another hour. The final paste (pH ≈ 11.5) was poured into a Teflon-lined autoclave and heated at 150 °C for 14 days. A white colored product was found at the bottom of the autoclave under a clear supernatant liquid. The product was washed with about 5 L of deionized water and then dried overnight in a vacuum oven at 100 °C. Na-ETS-4 thus synthesized was then subjected to ion exchange to replace its exchangeable monovalent Naþ with divalent Ba2þ ions in the following manner. A 0.5 M solution of barium chloride dihydrate (BaCl2 3 2H2O, Merck) was prepared by dissolving 122.16 g of the salt per liter of deionized water. About 15 g of Na-ETS-4 powder was added to ∼500 mL of the prepared salt solution. This mixture was boiled for an hour at 85 °C with continuous stirring. The mixture was then cooled to room temperature, and the clear supernatant liquid was decanted carefully from the top leaving the powder behind. The extent of cation exchange depends on the duration of boiling. The boilingcooling-supernatant-decanting cycle was repeated four times, each time with fresh barium salt solution to ensure maximum exchange. The exchanged sample, hereafter called Ba-ETS-4, was dried at 100 °C. The degree of exchange achieved was determined from energy dispersive X-ray (EDX) spectroscopic analysis. Physical Characterization. Three analytical tools, thermogravimetric analysis (TGA), X-ray diffraction (XRD), and field emission scanning electron microscope (FESEM), were used to characterize Ba-ETS-4. Similar analyses conducted on Na-ETS-4 and Sr-ETS-4 crystals have already been detailed in a previous communication from our laboratory.6 The thermal stability of Ba-ETS-4 was investigated by thermogravimetric analysis (TGA) (TA Instruments, TGA 2050 Thermogravimetric Analyzer) from room temperature to 600 °C under inert environment, that is, under a mild flow of nitrogen gas. Two different ramping rates of heating were used, 5 °C/min up to 400 °C and then 10 °C/min until the upper limit of the temperature range studied. Water loss profile for Ba-ETS-4 was qualitatively similar to that of Na-ETS-4 and Sr-ETS-4 reported earlier.6 Outgoing gas from TGA instrument was subjected to Fourier transform infrared (FTIR) (Bio-Rad FTS 3500 ARX FTIR mainframe) analysis. FTIR confirmed that the weight loss 3022

dx.doi.org/10.1021/ie1014124 |Ind. Eng. Chem. Res. 2011, 50, 3021–3034


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Figure 1. (a) Comparison of XRD signatures of (a) Na-ETS-4 and Ba-ETS-4 and (b) Ba-ETS-4 synthesized in this study with that reported in the patent literature (Kuznicki et al.3).

Figure 2. (a) XRD signatures of Ba-ETS-4 obtained with in situ heating at various temperatures and (b) crystallinity plots of both Na-ETS-4 and Ba-ETS-4 (crystallinity plot of Na-ETS-4 is taken from Marathe et al.6).

during heating was entirely due to water loss from the crystal structure. XRD diffraction data were obtained using Cu KR radiation in the 5-50° 2θ range with a scanning rate of 5 deg/min using a Shimadzu X-ray diffractometer (model Lab-X 6000). Samples were ground into very fine powder before XRD to minimize the effect of preferred orientation on the XRD pattern. A comparison of XRD signatures of Na-ETS-4 and Ba-ETS-4 is shown in Figure 1a. Substantial structural rearrangement of Na-ETS-4 took place after ion exchange indicated by the disappearance of some of the peaks including the strongest one (at ∼12.7° 2θ position) upon exchange. A major modification also took place at 2θ position of about 30°. A good agreement between the XRD signature of Ba-ETS-4 synthesized in this study and that reported in a patent literature3 was obtained, as may be seen from Figure 1b. XRD measurements were also carried out with in situ heating under vacuum at various predetermined temperatures, and the results are shown in Figure 2a. Peak width is related to the amount of amorphous phase in the material. The higher is the amorphous phase, the broader are the peaks. The XRD peaks of Ba-ETS-4 decreased in intensity and increased in breadth with progressive heating at higher temperatures, indicating progressive loss of crystallinity. Change in crystallinity of Ba-ETS-4 with temperature, which is an effect of water loss, was also studied, and the results are shown in Figure 2b. The percentage crystallinity was calculated by normalizing the integrated area under two strongest XRD peaks of Ba-ETS-4 sample heated at different temperatures with respect to that of Ba-ETS-4 heated at 100 °C. The crystallinity plot for Na-ETS-4 is also included in Figure 2b. Loss of crystallinity is related to loss of structural water, which occurred above 100 °C in both materials. Na-ETS-4 lost most of

its structural water at around 200 °C when its crystallinity started to drop rapidly. On the other hand, the structural water loss in Ba-ETS-4 was not complete until about 340 °C, which also delayed the sharp drop in crystallinity. The reason is that there is a direct chemical interaction between Ba2þ cations and the water molecules sitting near the cationic locations. As Ba2þ cations are bigger in size, the distance between these water molecules and cations is very small, and, therefore, there are strong interactions. On the contrary, being smaller in ionic size, Naþ cannot have much influence on the water molecules near the cationic locations. Difference in the cation size also explains why Ba-ETS-4 is thermally more stable than Sr-ETS-4 studied earlier.6 Crystal morphology of Ba-ETS-4 was obtained from FESEM (JEOL, model 6700F) study. An energy dispersive X-ray analysis (EDX) coupled with the FESEM gave the relative amounts of different elements present at the surface of the material in a selected point or area on FESEM image. EDX analysis confirmed complete ion exchange in Ba-ETS-4. There was no visible distinction between the morphology of Na-ETS-4 shown in a previous communication6 and that of Ba-ETS-4 observed in this study at the same magnification level. Replacement of one type of cation with another type can cause redistribution of ions between sublattices and can also alter the total water content. Such changes can, in turn, cause minor or significant framework distortions without altering the overall topology.15 Adsorbent Preparation. The very fine ion-exchanged BaETS-4 crystals synthesized in this study were pelletized (without any binder) in a hydraulic press by applying a pressure of 6 tons for 10 min. Sr-ETS-4 samples included in the binary study were similarly pelletized and reported earlier with the unary data on these samples.6,13 The weight and volume of the pellets were 3023



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Table 2. Effect of Dehydration Temperature on Adsorption and Diffusion of Gases in Ba-ETS-4 in the Linear Range of the Isotherm at 10 °C dehydration sample

temperature (°C)

adsorbate gas

K

KN2/KCH4

Ba-ETS-4

270

N2 CH4

132.80 365.90

0.36

350

N2

112.18

0.56

CH4

201.44

N2

100.59

400 450 a

CH4

29.89

N2

11.02

CH4

Dco/r2c (10-3 s-1)

(Dco,N2/r2c )/(Dco,CH4/r2c )

kinetic selectivitya

35.0 0.013

2692.3

18.7

15.9

2650

28.8

0.006 3.36

11.2

3733.2

205.3

1105.3

48.2

0.003 1.45

1.89

7.58

0.00171

Kinetic selectivity = KN2/KCH4 ((Dco,N2)/(Dco,CH4))1/2.

accurately measured, and the particle densities of as-synthesized, barium exchanged, and strontium exchanged adsorbents were 1.32, 1.72, and 1.53 g/cm3, respectively. The pellets were divided into smaller particles and were used for equilibrium and kinetic measurements. The particles had a bidispersed pore structure comprising intercrystalline macropores and intracrystalline micropores. To study the effect of dehydration temperature on pore shrinkage and therefore on gas adsorption and diffusion in the shrunken pores, Ba-ETS-4 particles were dehydrated at 270, 350, 400, and 450 °C in a furnace for 15-16 h under helium flow at atmospheric pressure. These samples will be called Ba270, Ba350, Ba400, and Ba450, respectively, in the following sections for easy reference. Prior to every experimental run for measuring adsorption equilibrium and kinetics, the adsorbent samples were further regenerated in situ at 190-200 °C for 10-11 h under vacuum. Particular care was taken to periodically flush the system with helium to increase the effect of regeneration. Measurement of Unary Equilibrium and Kinetics. Following adsorbent preparation, the constant volume method was used to measure unary equilibrium and differential uptake rates for pure methane and nitrogen in the Ba-ETS-4 samples over a range of pressures (from very low in the linear range of the isotherm to about 8 bar) and temperatures (-18 to 50 °C). The constant volume apparatus, measurement procedures, and data processing techniques have been detailed elsewhere6,16 and therefore are not repeated here. The amount of the adsorbent samples used in the constant volume experiments was approximately 11 g after regeneration. Measurement of Binary Equilibrium and Kinetics. A differential adsorption bed (DAB) was used to measure binary equilibrium and integral uptakes of three different nitrogen-methane mixtures in Ba400, Sr190, and Sr270. 50:50 and 90:10 CH4:N2 mixtures were used for Ba400, and the measurements were conducted at 10 °C. For Sr190 and Sr270, measurements were carried out with 50:50 and 10:90 CH4:N2 mixtures at 30 °C. The DAB method of multicomponent equilibrium and kinetic measurements has been discussed in many publications.17-20 For a comprehensive description of the setup, measurement procedures, and data processing techniques, the readers may consult the dissertation by Bhadra21 from our laboratory. The amount of adsorbent samples used in the DAB experiments was about 1 g.

’ THEORETICAL SECTION Adsorption Equilibrium. The unary adsorption equilibrium data were analyzed using the Langmuir and multisite Langmuir isotherm (MSL) models. Equation 1 below is the general multicomponent

form of the multisite Langmuir model: bi ci ¼

qi =qsi n P ð1 qi =qsi Þai

ð1Þ

i¼1

The model assumes that an adsorbent has a fixed number of sites (qs) and that an adsorbate molecule, depending on its size and orientation in the adsorbed phase, occupies a certain number of these adsorption sites (qi). Therefore, for thermodynamic consistency:22 qs ¼ qsi ai ¼ constant

ð2Þ

where qsi is the saturation capacity of each adsorbate. ai and qsi are independent of temperature, and bi, the isotherm constant, has the Arrhenius form of temperature dependence given by bi ¼ ðbo Þi e - ΔUi =Rg T

ð3Þ

The multisite Langmuir model reduces to the Langmuir model when ai = 1. The multisite Langmuir model, therefore, relaxes the impractical requirement of equal saturation capacity of all the components in a mixture for the multicomponent extension of the Langmuir model to be thermodynamically consistent. Adsorption Kinetics. As mentioned earlier, the single component differential and binary integral uptakes were measured in a constant volume apparatus and a differential adsorption bed, respectively. The mathematical models used to analyze the experimental uptake results from these two types of experiments are detailed in the Appendix.

’ RESULTS AND DISCUSSION Effect of Dehydration Temperature on Equilibrium and Kinetics. The linear range equilibrium data and diffusional time

constants of nitrogen and methane in Ba-ETS-4 measured at progressively increasing dehydration temperature are summarized in Table 2. The corresponding equilibrium isotherms up to ∼7 bar and uptake plots measured in the linear range of the isotherm are shown in Figures 3 and 4, respectively. Dehydration of Ba-ETS-4 led to pore shrinkage, which in turn affected the equilibrium and kinetics of adsorbing gases. Decrease in diffusivity value with increasing dehydration temperature, as seen from Table 2, is the most direct evidence of shrinking size of the pores through which transport takes place. The amount of adsorbate adsorbed in the adsorbent pores depends on the depth of the potential well, which is a complex function of the pore size, molecular size of the adsorbate, and charge distribution in the adsorbent framework. It is clear from 3024



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Figure 3. Effect of dehydration on (a) nitrogen and (b) methane isotherms on Ba-ETS-4 measured at 10 °C.

Figure 4. Low coverage uptakes of (a) nitrogen and (b) methane Ba-ETS-4 dehydrated at various temperatures. The uptakes were measured at 10 °C.

the Henry’s constant data in Table 2 and the isotherms in Figure 3 that methane was initially more strongly adsorbed than nitrogen. Shrinking pore with increasing dehydration temperature reduced the pore potential for adsorption, which caused the drop in Henry’s constants and the isotherms. However, the effect appears to have been more for the bigger methane molecule than the relatively smaller nitrogen molecule. As such, although the methane isotherm was initially stronger, ultimately after a certain dehydration temperature there was a reversal in equilibrium and nitrogen became the preferred adsorbate. Significant reversal occurred at 400 °C, and adsorption capacity became negligible beyond dehydration temperature of 450 °C due to significant loss of crystallinity. On the other hand, methane diffusivity was much slower than nitrogen diffusivity in the beginning. The diffusivities of nitrogen and methane also decreased with increasing dehydration temperature due to pore contraction, change in water occupancy in the pores, and relocation of the exchanged cations.11 However, the diffusivity ratio (nitrogen over methane) was practically constant until 400 °C, after which there was a drastic drop. From Figure 4a it is obvious that this drastic drop is due to the significant reduction of nitrogen uptake rate. As such, the kinetic selectivity went through a maximum as the dehydration temperature was increased. Ba400, dehydrated at 400 °C, gave the maximum selectivity of ∼205. This selectivity of nitrogen over methane is much higher than the best value reported in the literature.6,23,24 Having identified the condition that gave a very high selectivity of nitrogen over methane, the next step was to conduct a very detailed equilibrium and kinetic study of the two gases in the sample, which is discussed next. Single Component Equilibrium in Ba400. Equilibrium isotherms of nitrogen and methane were measured on Ba400 at three different temperatures over a wide pressure range. The Langmuir and multisite Langmuir models were fitted to the measured

isotherm data. Langmuir model parameters were extracted by separately fitting the experimental isotherms for each component at three different temperatures to eqs 1-3 by allowing qsi, (bo)i, and ΔUi as the fitting parameters. Nitrogen and methane data were fitted independently. Isotherm parameters for the multisite Langmuir model were extracted by simultaneous nonlinear regression of nitrogen and methane data at all available temperatures with the constraint that aiqsi(=qs) is equal for both of the gases. The quantity qs is the total number of adsorption sites per unit volume of the adsorbent, and it must be independent of adsorbate to satisfy thermodynamic consistency.22 Seven parameters, ai, (bo)i, ΔUi (for the two components), and the common qs, were extracted by fitting the model to the experimental data. In both of the isotherm models, the theoretical adsorbed amount is a nonlinear function of the fitted parameters. It was formulated as a nonlinear optimization problem and was solved using the subroutine DBCONF in IMSL (International Mathematical Statistical Library), which used a quasi-Newton method and a finite-difference gradient to minimize a function of N variables subjected to bounds on the variables. Because the multisite Langmuir model is implicit in the theoretical adsorbed amount, the nonlinear equation solver subroutine DNEQNF in IMSL was also used in conjunction with the optimization subroutine. During residual minimization, initial guesses were systematically varied to ensure that the smallest possible residuals were reached. The optimized model parameters and the corresponding residuals are given in Table 3 from which it is clear that the multisite Langmuir isotherm model gives much better fits to the experimental data as compared to that by the Langmuir isotherm model. Multisite Langmuir model fits of the experimental equilibrium data are shown in Figure 5. 3025



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Table 3. Equilibrium Isotherm Parameters for Nitrogen and Methane on Ba-ETS-4 Dehydrated at 400 °Ca model Langmuir multisite Langmuir a

bo, cc/mmol

(-ΔU), kcal/mol

N2

0.0078

4.45

CH4

0.0679

3.25

N2

0.0076

CH4

0.1228

adsorbate

a

qsi, mmol/cc

residual

1

2.40

0.1230

1

0.86

0.0322

4.16

3.33

4.41

0.0010

2.30

5.54

2.65

0.0007

1 kcal/mol = 4.1868 kJ/mol.

Figure 5. Multisite Langmuir isotherm model fits of (a) nitrogen and (b) methane equilibrium data at various temperatures on Ba400.

Figure 6. Uptake of (a) nitrogen and (b) methane in Ba400 at different temperatures at low coverage and corresponding optimum model fits.

Single Component Kinetics in Ba400. The theoretical model used to analyze the single component kinetic data has been detailed in the Appendix. The micropore diffusional time constant was the only unknown in the model, which was extracted by minimizing the residual between the model fit and experimental data. Representative optimum fits of the model to experimentally measured uptakes of nitrogen and methane in Ba400 in the linear range of the isotherm at different experimental temperatures are shown in Figure 6, and the extracted diffusivity values are compiled in Table 4. It is clear that the prepared bidispersed model with molecular diffusion in the macropores and pore diffusion in the micropores can adequately capture the experimentally observed uptake behavior. Transport of gas molecules between the crystalline microparticles is an activated process. Diffusion in the micropore is known to follow Eyring-type temperature dependency. This has the following form:

Dco ¼ D0 co e - Ed =Rg T D0co

ð4Þ

where is the pre-exponential constant, and Ed is the activation energy of diffusion. The activation energies extracted from the Eyring plots are 9.1 and 9.0 kcal/mol (see Table 4) for

Table 4. Temperature Dependence of Equilibrium and Kinetic Parameters Ba-ETS-4 Dehydrated at 400 °Ca Ed,

Henry’s adsorbate N2

CH4

a

temperature, (°C)

constant, K

Dco/r2c , s-1

-17.7

243.14

2.30 10-3

10.0

100.62

11.2 10-3

30.0 10.0

49.93 29.89

39.7 10-3 3.12 10-6

30.0

20.38

9.0 10-6

50.0

14.25

22.5 10-6

kcal/mol 9.1

9.0

1 kcal/mol = 4.1868 kJ/mol.

nitrogen and methane, respectively. It is interesting to note that, while the diffusivities of nitrogen and methane are still quite different in the contracted pores of Ba-ETS-4, their activation energies are very close. To investigate the nature of the concentration dependence of micropore diffusivity of gases in the contracted pores of Ba-ETS-4, differential uptakes of methane were measured in Ba400 at various levels of adsorbate loading. The corresponding theory based on 3026



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Figure 7. Concentration dependence of micropore diffusivity of methane in Ba400. Plots (a) and (b) are based on Langmuir and multisite Langmuir parameters, respectively. The solid lines in (a) and (b) are the plots of eqs A.15 and A.14, respectively.

Figure 8. Experimental results and multisite Langmuir model predictions for binary isotherms of (a) 50:50 and (b) 90:10 CH4:N2 mixture in Ba400 at 10 °C.

the chemical potential gradient as the driving force for diffusion, discussed in the Appendix, suggests that the concentration dependence is independent of temperature. Hence, the temperature was also varied in addition to adsorbate loading. Concentration dependence of nitrogen could not be measured because its kinetics was very fast even when the temperature was lowered to -18 °C. The experimental results are compared to the theoretical predictions for the Langmuir isotherm (eq A.15) and multisite Langmuir isotherm (eq A.14) in Figure 7. Both of the predictions capture the correct qualitative trend of the experimental results. The improvement brought about by the multisite Langmuir isotherm fit of the equilibrium data does not seem to significantly impact the prediction of the concentration dependence of micropore diffusivity. In fact, the two predictions are quantitatively quite similar. This is not totally unexpected because the improvement in the fit of the equilibrium data is not so much for methane as it is for nitrogen. Despite the quantitative similarity of the two predictions, the multisite Langmuir isotherm is the preferred choice in view of its clear overall superiority in representing the equilibrium data and is tested further with binary results in the following sections. Binary Equilibrium. The experimental binary equilibrium isotherms for 50:50 and 90:10 CH4:N2 mixtures on Ba400 measured at 10 °C are shown in Figure 8. Isotherms for 50:50 and 10:90 CH4:N2 mixtures on Sr270 and Sr190 samples at 30 °C have also been included in this Article, which are shown in Figures 9 and 10. Results from repeat runs showed excellent reproducibility. Multisite Langmuir model predictions using single component equilibrium isotherm parameters are also presented in these figures. The parameters for Ba400 are given

in Table 3, and for Sr190 and 270 are taken from Table 1 of our unary study on these two samples published earlier.13 For 50:50 CH4:N2 mixture on Ba400, the deviations between the experimental data and model predictions are rather large. The nitrogen isotherm is overpredicted, and the methane isotherm is grossly underpredicted. The situation is somewhat better for 90:10 CH4:N2 mixture. A closer observation reveals that there is very little effect of the presence of nitrogen on methane adsorption. Incidentally, natural gas upgrading typically involves methane-nitrogen mixture containing 10-15% nitrogen. Hence, it should be quite reasonable to choose MSL as the isotherm model in uptake and process studies related to natural gas upgrading. In both adsorbents, Sr270 and Sr190, for 50:50 CH4:N2 mixture the measured equilibrium of nitrogen was lower than the MSL model isotherm prediction, the difference being more significant in Sr270, as may be seen from Figure 9. In both cases, the deviation increased with increasing pressure. However, methane isotherm was much closer to the MSL prediction. In Sr190, the theoretical predictions were somewhat higher than the experimentally measured results for both methane and nitrogen. Mitchell et al.,25 in their simulation study, have reported that the presence of methane does have a significant influence on the adsorption of the other component in a binary mixture in ETS-4 and zorite. It should be recalled here that Sr190 has slightly bigger pores than Sr270, a fact clearly demonstrated from the lower diffusivities of all adsorbates in the latter as compared to those in the former. In the pores of adsorbate dimensions, there appears to be some additional repulsive interaction between nitrogen and methane under binary conditions leading to isotherm depression. Clearly, the extent of interaction is dependent on both pore size and level of concentration. In Sr270, nitrogen 3027



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Figure 9. Experimental results and multisite Langmuir predictions for binary adsorption of 50:50 CH4:N2 mixture in (a) Sr270 and (b) Sr190 at 30 °C.

Figure 10. Experimental results and multisite Langmuir predictions for binary isotherms of 10:90 CH4:N2 mixture in (a) Sr270 and (b) Sr190 at 30 °C.

Figure 11. Experimental results and theoretical predictions for binary uptake of (a) 50:50 and (b) 90:10 CH4:N2 mixtures in Ba400 at 10 °C and 7 bar.

equilibrium was severely affected by the presence of methane at high concentration. It is seen from Figure 10 that with only 10% methane, the measured and predicted isotherms were in very good agreement in case of Sr190. However, in Sr270, methane, even at 10% level, seemed to affect nitrogen adsorption, and the deviation increased with increasing feed pressure. Binary Diffusion. Binary integral uptake of 50:50 and 90:10 CH4:N2 mixtures in Ba400 was measured at 7 bar and 10 °C. The experimental results along with the repeat runs are shown in Figure 11. The predicted uptakes according to the model presented in the Appendix are also shown in Figure 11. The features of the diffusion model are bidispersity in pore structure having molecular diffusion in the macropore, concentrationdependent micropore diffusion with chemical potential gradient as the driving force for diffusion, and adsorption equilibrium at the micropore surface following multisite Langmuir isotherm.

The equilibrium and diffusion parameters are given in Tables 3 and 4, respectively. Like binary equilibrium results, binary integral uptake measurements conducted in Sr270 and Sr190 samples are also included in this Article. Experimentally measured uptakes for the 50:50 N2:CH4 gas mixture are compared to the theoretical predictions (from the same diffusion model used for Ba400) in Figure 12. The measurements were done at 10 bar pressure at a temperature of 30 °C. In Figure 12a, run 2 stands for the fractional uptakes calculated by normalizing with the number of moles from the repeated equilibrium run, while in Figure 12b, run 2 stands for repeated uptake measurements. In both adsorbents, Sr270 and in Sr190, there was excellent agreement between the normalized experimental uptake results and the theoretical predictions. Despite the large deviation in binary equilibrium predictions, particularly for the 50:50 mixture, it is indeed very encouraging 3028



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Figure 12. Experimental results and theoretical predictions for binary uptake of 50:50 CH4:N2 mixture in (a) Sr270 and (b) Sr190 at 30 °C and 10 bar. In (a) run 2 stands for the fractional uptakes calculated by normalizing with the number of moles from the repeated equilibrium run, while in (b) run 2 stands for repeated uptake measurements.

Figure 13. Experimental results and theoretical predictions for effective N2/CH4 separation selectivity for (a) 50:50 and (b) 90:10 CH4:N2 mixtures at 10 °C and 7 bar in Ba400. Ideal kinetic selectivity is also shown for reference. The first few data points give infinite selectivity because methane adsorption was undetectable in the early part of the uptake.

that uptake results are reasonably well predicted by the model including the roll-up of nitrogen. Because nitrogen is the faster diffusing component, it reaches the micropore interior much ahead of methane and attains a loading higher than the limit of binary equilibrium. The excess is eventually displaced by the slower diffusing methane giving rise to the roll-up of nitrogen. It is also very interesting to note that the depression of nitrogen equilibrium in the presence of methane in the small pores of Ba400, Sr270, and Sr190 does not seem to significantly affect the plot of normalized uptake versus time. Effective Separation Selectivity. A proper definition of separation factor in a kinetically controlled adsorption separation process is given by eq 5. It is clear from the equation that kinetic selectivity is time-dependent. However, the comparative study of kinetic selectivity of nitrogen over methane in progressively contracting pores of Ba-ETS-4 samples presented earlier was based on eq 6. ! ! qc ðtÞ qc co qc !A !A ð5Þ ηK , AB ¼ qc ðtÞ qc co qc B B sffiffiffiffiffiffiffiffiffiffiffiffiffi KA ðDco ÞA ηK, AB ¼ ð6Þ KB ðDco ÞB Equation 6 is a reduction of eq 5 under the following three major assumptions: (i) short contact times, (ii) uncoupled diffusion,

and (iii) linear or Langmuir isotherm. In addition to these assumptions, eq 6 only accounts for the loading in the micropores and completely ignores the nonselective storage capacity of the macropores. In this section, the adsorbent samples are reassessed by investigating the time-dependent selectivity using the detailed bidispersed binary diffusion model based on multisite Langmuir isotherm and chemical potential gradient as the driving force for diffusion validated in the previous section with experimental binary integral uptake results. According to the chemical potential gradient theory, the diffusional interaction in a multicomponent system is a result of the coupled nonlinear equilibrium relationships of the adsorbates. The expression for the selectivity after relaxing all the assumptions leading to eq 6 is as follows: ! qp ðtÞ co !A ð7Þ effective selectivity ¼ qp ðtÞ co B

The time-dependent, effective selectivities of nitrogen over methane in Ba400 according to eq 7 for the two methane-nitrogen mixtures studied are compared to experimental results measured at 10 °C in Figure 13. The ideal kinetic selectivity (i.e., uncoupled kinetic selectivity given by eq 6) is also included in the figure for comparison. It is evident from the figure that for both mixtures, the selectivity passes through a maximum at a short contact time, and then it gradually approaches the equilibrium selectivity limit. The theoretical maximum value attained is 3029



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Figure 14. Experimental results and theoretical predictions for effective nitrogen/methane separation selectivity for a 50:50 CH4:N2 mixture in (a) Sr270 and (b) Sr190 at 30 °C and 10 bar. Ideal kinetic selectivity is also included for reference.

higher for the 90:10 CH4:N2 mixture, although it is still far below the ideal selectivity value, which is expected because the former takes into account the nonselective capacity of the adsorbent macropores. As for the experimental results, the first few data points give infinite selectivity because methane adsorption was undetectable in the early part of the uptake. This most likely was due to the limitation of the GC analysis system. These points in the early part of the uptake are, therefore, not shown in Figure 13. The large deviation between the experimental and predicted results in Figure 13a is due to a similar deviation in methane uptake shown in Figure 11a. Like the ideal selectivity of >200, the maxima in the effective selectivity showing a value over 30 for 90:10 CH4:N2 mixture is also considered very high as compared to other known adsorbents. Moreover, the decay in the effective selectivity beyond the peak value is slow, which means that Ba400 will enjoy some flexibility with cycle time if used in a PSA process for natural gas upgrading. The experimental and theoretical separation selectivities for a 50:50 N2:CH4 gas mixture in Sr270 and Sr190 are shown as a function of time in Figure 14. Ideal selectivity is also shown for easy reference. The ideal selectivity is significantly higher than the maximum effective selectivity in both Sr270 and Sr190. As can be seen from the figure, in Sr270, the theoretical effective selectivity significantly exceeded the selectivity calculated from experimental data. This resulted from the lower (suppressed) nitrogen isotherm in Sr270 as compared to the multisite Langmuir model prediction. The experimental selectivity reached a maximum value of about 2 at short contact time, after which it steadily dropped to a value nearly equal to unity as equilibrium approached. For adsorption in Sr190, there was good agreement between the theoretical effective selectivity and that calculated from experimental data. This was expected from better fits of the binary experimental isotherm as well as uptake data to the theoretical predictions. At short contact times, the selectivity reached a value of about 4.5 and then dropped quickly to about 2 and finally below 1 near equilibrium. The somewhat lower experimental selectivity in Sr190 may also be a result of the suppressed nitrogen isotherm similar to that in Sr270. The sharp peak in the selectivity plot of Sr190 indicated that, to exploit the higher selectivity, cycles employing this adsorbent will need to be short. Simulation results also showed that in both Sr270 and Sr190, changes in system temperature and pressure had an insignificant effect on the effective separation selectivity. In Table 5, calculated maximum effective selectivity values are compared to the ideal values for Sr190 and Sr270 at several temperatures for the adsorption of a 50:50 mol % N 2 :

Table 5. Ideal and Effective Selectivity for Nitrogen/Methane Separation in Sr-ETS-4 Samples sorbent temperature (°C) ideal selectivity maximum effective selectivity Sr270

Sr190

0.0

7.83

4.61

10.0

11.89

4.72

30.0

12.34

4.84

0.0

7.85

6.68

10.0

6.66

6.58

30.0

8.12

6.18

CH4 mixture at 10 bar pressure. It is clear that the maximum effective selectivity is greater in Sr190 than in Sr270, although Sr270 shows higher ideal selectivity values. This observation is experimentally well supported from the results in Figure 14. The limitations of the ideal selectivity (calculated using eq 6) to represent the separation factor exhibited by an adsorbent have been highlighted. It has been shown that the effective selectivity taking into consideration equilibria and diffusional interaction will provide a better indication of kinetic separation potential of an adsorbent.

’ CONCLUSIONS Ba-ETS-4 crystals were obtained by completely exchanging the Naþ ions in Na-ETS-4, synthesized in our laboratory following a published recipe, with Ba2þ ions. In view of their importance in natural gas upgrading, adsorption and diffusion of methane and nitrogen were measured in Ba-ETS-4 samples dehydrated at progressively increasing temperatures. Initially, at lower dehydration temperature, methane was stronger in adsorption and slower in diffusion than nitrogen. Progressive dehydration reduced equilibrium capacity as well as rate of diffusion for both of the gases. The effect was greater on the bigger methane molecule than the relatively smaller nitrogen molecule. The diffusivity ratio increased, and the equilibrium selectivity decreased. Ultimately, there was a reversal in equilibrium selectivity leading to a maximum in kinetic selectivity. A value of 205 for ideal kinetic selectivity was obtained for the Ba400 sample dehydrated at 400 °C. The multisite Langmuir model well represented the unary equilibrium and kinetic data of methane and nitrogen in Ba400. The bidispersed pore diffusion model, assuming molecular diffusion in the macropores and micropore diffusivity as the fitting parameter, successfully captured the differential uptake data measured at different temperatures and various level of adsorbate loading. 3030


Industrial & Engineering Chemistry Research The micropore diffusivity was concentration dependent, and Darken’s equation (based on the chemical potential gradient as the driving force for diffusion) corresponding to multisite Langmuir isotherm was able to explain the experimental trend. The validity of the binary extensions of the unary equilibrium and kinetic models (using parameters obtained from independent unary measurements) was confirmed with experiments on two different mixtures of methane and nitrogen, one equimolar and the other rich in methane. The actual equilibrium values for nitrogen were somewhat lower than the predicted values, but the presence of nitrogen did not seem to have a significant effect on methane adsorption. The predictions were better for high methane content in the mixture. In contrast, for Sr270 and Sr190, the equilibrium capacities measured from the equimolar feed mixture were lower for both of the gases as compared to the model predictions. Lowering the methane content in the feed gas mixture did improve the difference between theory and experiment, particularly in Sr190. Interestingly, predictions of the binary kinetic model (presented as normalized uptake) were very encouraging for all the mixtures used for all three adsorbent samples (Ba400, Sr270, and Sr190) reported in this Article, despite a somewhat unsatisfactory equilibrium prediction for the equimolar mixture. The importance of incorporating the equilibrium and kinetic interactions under binary conditions, higher adsorbate loading, and longer contact time on the nitrogen/methane separation selectivity was demonstrated. The effective selectivity accounting for the above three factors gave a more realistic representation of the separation potential of the adsorbents explored as compared to ideal selectivity. The experimentally verified binary models capturing transport of methane and nitrogen in one Ba-ETS-4 and two Sr-ETS-4 samples presented here have been used to compare their performance in a kinetically controlled pressure swing adsorption process for natural gas upgrading. The results will be communicated in the future.

’ APPENDIX: THEORETICAL MODEL FOR ADSORPTION KINETICS The adsorbent particles were made by binding the crystals under pressure. Hence, the particles had a bidispersed pore structure. The bidispersed pore diffusion model used to analyze differential uptake measured in the constant volume apparatus and integral uptake measured in the DAB apparatus had the following assumptions: (1) The system was isothermal, and the ideal gas law was valid. (2) A film resistance separated the external fluid from the particle surface in binary experiments. Both macro- and microparticles were assumed spherical. (3) The adsorbate transport in the macropores was by molecular diffusion. (4) Gradient in chemical potential was the driving force for diffusion in the micropores. A large value was assigned to the external film coefficient to numerically approximate its negligible contribution in mixture study in the DAB method where the adsorbate flow was kept high. This approach gave flexibility and was preferred over applying the equilibrium boundary condition at the adsorbent solid surface.

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Macroparticle mass balance for component i: " # ∂cpi ∂2 cpi 2 ∂cpi ∂qci þ ð1 - εp Þ ¼ εp D p þ εp ∂t ∂t ∂R 2 R ∂R

ðA.1Þ

Boundary conditions at the macroparticle center and the macroparticle surface: ∂cpi ∂R

¼ 0

ðA.2Þ

R¼0

∂cpi εp D p ∂R

¼ kf ðcoi - cpi jR ¼ Rp Þ

ðA.3Þ

R ¼ Rp

In the above equations, hqc is the average adsorbed phase concentration in the micropores, cp is the gas concentration in the macropore, co is the bulk gas concentration, Dp(=Dm/τ) is tortuosity (τ) corrected molecular diffusivity in the macropore, kf is the external fluid film coefficient, εp is the adsorbent macroporosity, Rp is the particle radius, R is the radial distance in the macroparticle, and t is time. In eq A.1: ∂qci 3 ¼ - Ji jr ¼ rc rc ∂t

ðA.4Þ

where J is the flux of a diffusing component in the microparticles and rc is the microparticle radius. Microparticle mass balance for component i: ∂qci 1 ∂ ¼ 2 fr 2 ðJi Þg r ∂r ∂t

ðA.5Þ

qc is the adsorbate concentration in the micropores, and r is the distance along the microparticle radius. Starting from chemical potential gradient as the driving force for diffusion and by introducing an imaginary gas-phase concentration, which is in equilibrium with the adsorbed phase concentration in the micropores (Hu and Do26), the following equation is obtained: Ji ¼ - ðDc Þi ¼ ðDco Þi

∂qci ∂r

d ln cim i ∂qci d ln q ∂r

¼ ðDco Þi

qci ∂cim i cim ∂r i

ðA.6Þ

In the above equation, (Dc)i is the concentration-dependent micropore diffusivity, (Dco)i is the limiting diffusivity in the linear range of the isotherm, qi is the adsorbed concentration at a position r in the micropore, and cim i is the imaginary gas-phase concentration in equilibrium with qci. Microparticle mass balance after substituting A.6 in A.5: ( !) ∂qci 1 ∂ 2 qci ∂cim i r ðDco Þi im ¼ 2 r ∂r ∂t ci ∂r 3031

ðA.5aÞ



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Boundary conditions at the center and the surface of the microparticle: ∂cim i ¼ 0 ðA.7Þ ∂r

Dose cell mass balance: Vd

r¼0

cim i jr ¼ rc ¼ cpi

ðA.8Þ

The imaginary gas-phase concentrations, cim i , can be calculated from the isotherm model used. In the present case, the multisite Langmuir model was used. Equation 1 is the multisite Langmuir model. DAB Method. In the DAB experiments, the bed length was short (a few adsorbent particles), and a high flow rate was used. This justified the assumption that fluid phase concentration remained practically unchanged. Therefore, coi in eq A.3 was taken as equal to the component concentration in the feed. Constant Volume Method. In the constant volume method, the system pressure was a function of time. Therefore, coi was not constant like in the DAB experiments. The following additional differential mass balance equationss (eqs A.9-A.13) were necessary in conjunction with eqs A.1-A.8 to determine the diffusional time constant from the uptake experiments conducted in the constant volume apparatus. Because use of this method was limited to only pure gas, component concentration variables are written without subscript i in the rest of this subsection. The following relation was used to account for any influence of the solenoid valve on the measured adsorption uptake: dnv ¼ XðPd - Pu Þ dt

ðA.9Þ

where nv is the number of moles of gas flowing through the valve, and X is the valve constant, Pd is the time-dependent pressure on the dose side, and Pu is the time-dependent pressure on the test side. The validity of the linear driving force assumption for the gas flow through the solenoid valve was examined in a previous study in this laboratory.27 A constant value was obtained for X (=0.04 mol bar-1 s-1) from blank runs (i.e., without any adsorbent in the test chamber) using different gases at various temperatures. It was concluded that the type of solenoid valve used in the constant volume setup of this laboratory did not offer any significant unexpected additional dynamics to the overall transport of the adsorbates. The constancy of the valve constant was also confirmed in an earlier study in this laboratory,13 but the value obtained was somewhat different (0.085 mol bar-1 s-1). During data analysis, it was found that the magnitude of the valve resistance (either value) did not have any impact on the extracted kinetic data. Uptake cell mass balance: 0 Dp dcp dPu @ ¼ R g T - 3 εp V a εVu dt Rp dR Pu jt ¼ 0 ¼ Pu0

R ¼ Rp

1 dnv A þ dt

ðA.10Þ ðA.11Þ

where Vu is the empty test chamber volume, Va is the adsorbate volume, and ε is the fraction of the test chamber not occupied by the adsorbent.

dPd dnv ¼ - Rg T dt dt

ðA.12Þ

Pd jt ¼ 0 ¼ Pd0 þ

ðA.13Þ

There was no external fluid film resistance in the constant volume measurements with a pure gas, and the following boundary condition was used in place of eq A.3: Pu ðA.3aÞ cp jR ¼ R p ¼ co ¼ Rg T For single component differential uptake measurements conducted in the constant volume apparatus, the change in adsorbent loading was minimal. Therefore, it was assumed that the micropore diffusivity was approximately constant (not the same) in each run, which reduced eqs A.5a, A.7, and A.8 to the following equations: ∂qc 1 ∂ 2 ∂qc r ¼ ðDc Þ 2 ðA.5bÞ r ∂r ∂t ∂r ∂qc ¼ 0 ðA.7aÞ ∂r r¼0

qc jr ¼ rc ¼ f ðcp Þ

ðA.8aÞ

In eq A.8a, f(cp) represents the equilibrium isotherm model. In the differential uptake measurements, it was assumed that the segment of the isotherm covered by the small step pressure change introduced in each run could be approximated by a straight line. This linear assumption and a suitable choice of reference for non-dimensioning q provided a linear relationship between the dimensionless adsorbate concentration at the microparticle surface and the corresponding dimensionless gas concentration in the macropore. For a single component multisite Langmuir isotherm, the relationship between the concentration-dependent micropore diffusivity, Dc, and the limiting diffusivity in the linear range of the isotherm, Dco, is given by the following equation: Dc 1 þ θða - 1Þ ¼ 1-θ Dco

ðA.14Þ

which simplifies for a Langmuir isotherm (a = 1) to: Dc 1 ¼ 1-θ Dco

ðA.15Þ

In eqs A.14 and A.15, θ = qc*/qsi. Use of subscript i is necessary here to highlight the distinction between qs and qsi in the multisite Langmuir model (see eq 2). Solution Method. The variables in the model equations were non-dimensionalized. The equations were then discretized in space using the method of orthogonal collocation, thereby reducing the set of coupled partial differential equations to a set of ordinary differential equations, which were then integrated in the time domain using a standard Gear’s variable step integration routine. 16 collocation points each along the macroparticle and microparticle radii were used for the discretization. The concentration profiles in the macroparticles and microparticles were then integrated over the respective volumes, and 3032



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the uptake was calculated as: R1 R1 εP 0 3cpi ðtÞχ2 dχ þ ð1 - εP Þ 0 3qci ðtÞχ2 dχ qpi ðtÞ ¼ ðA.16Þ qpi qpi where

Z qci ðtÞ ¼

1

qci ðtÞη2 dξ

ðA.17Þ

0

In eq A.16, qpi(t) is the adsorbed amount of component i at a certain time at a dimensionless position η along the particle radius, and q*Pi is the amount of component i adsorbed at equilibrium, both based on particle volume. χ (=R/RP) and ξ (=r/rc) are the dimensionless distances along macroparticle and microparticle radii, respectively. q*Pi is related to the crystal volume-based equilibrium capacity, q*Pi, by the following equation: qpi

¼

εp coi þ ð1 - εp Þqci

ðA.18Þ

A typical macropore voidage value of 0.4 was assumed in the above equation.

’ AUTHOR INFORMATION Corresponding Author

*Tel.: 65-65166545. Fax: 65-67791936. E-mail: chesf@nus. edu.sg.

’ ACKNOWLEDGMENT This work was carried out under the research projects R279000116112 and R279000174112, both funded by the Ministry of Education, Singapore. ’ NOTATION a = adsorption sites occupied by each molecule in the adsorbed phase b = Langmuir constant, cc/mmol bo = pre-exponential constant for temperature dependence of b, cc/mmol c = gas-phase concentration, mmol/cc cim = imaginary gas-phase concentration in equilibrium with qc, mmol/cc co = gas concentration in the external fluid phase, mmol/cc cp = gas concentration in the macropore, mmol/cc CT = total concentration of a gas mixture, mmol/cc Dc = micropore diffusivity, cm2/s Dco = limiting micropore diffusivity, cm2/s D0co = pre-exponential constant for temperature dependence of Dco, cm2/s Dm = molecular diffusivity, cm2/s Dp = tortuosity corrected molecular diffusivity in macropores, cm2/s Ed = activation energy for micropore diffusion, kcal/mol J = diffusive flux in micropores, mol/cm2 3 s K = dimensionless Henry’s constant kf = fluid phase mass transfer coefficient, cm/s nv = number of moles flown through the valve separating dose and test sides of the constant volume apparatus, mol P = pressure, bar q = adsorbed phase concentration, mmol/cc qs = monolayer saturation capacity according to the Langmuir or

multisite Langmuir model, mmol/cc qsi = saturation capacity of each adsorbate according to the multisite Langmuir model, mmol/cc q* = adsorbed amount in equilibrium with co, mmol/cc hq = average concentration in the adsorbed phase, mmol/cc r = radial distance coordinate of microparticle, cm rc = microparticle radius, cm R = radial distance coordinate in the macroparticle, cm Rg = universal gas constant Rp = radius of adsorbent particle, cm t = time, s T = temperature, K ΔU = change of internal energy due to adsorption, kcal/mol V = volume, cc X = valve constant, mol/bar s Greek Letters

χ = dimensionless macroparticle radial distance (=R/Rp) εp = particle voidage (-) ηk = kinetic selectivity (-) θ = fractional coverage of the adsorption sites (-) τ = tortuosity (-) ξ = dimensionless microparticle radial distance (=r/rc) Subscripts and Superscripts

a = adsorbent c = per unit microparticle volume d = dose tank i = ith component (A, component A; B, component B; CH4, methane; N2, nitrogen) p = per unit particle volume u = test tank 0 = initial value in the test tank 0þ = initial value in the dose tank

’ REFERENCES (1) Kuznicki, S. M. Large-Pore Crystalline Titanium Molecular Sieve Zeolites. U.S. Patent 4,853,202, 1989. (2) Kuznicki, S. M. Preparation of Small-Pored Crystalline Titanium Molecular Sieve Zeolites. U.S. Patent 4,938,939, 1990. (3) Kuznicki, S. M.; Bell, V. A.; Petrovic, I.; Blosser, P. W. Separation of Nitrogen with Mixtures Thereof with Methane Utilizing Barium Exchanged ETS-4. U.S. Patent 5,989,316, 1999. (4) Miraglia, P. Q.; Yilmaz, B.; Warzywoda, J.; Bazzana, S.; Sacco, A., Jr. Morphological and Surface Analysis of Titanosilicate ETS-4 Synthesized Hydrothermally with Organic Precursors. Microporous Mesoporous Mater. 2004, 69, 71. (5) Yang, R. T. Adsorbents: Fundamentals and Applications; John Wiley & Sons: New Jersey, 2003. (6) Marathe, R. P.; Mantri, K.; Srinivasan, M. P.; Farooq, S. Effect of Ion Exchange and Dehydration Temperature on the Adsorption and Diffusion of Gases in ETS-4. Ind. Eng. Chem. Res. 2004, 43, 5281. (7) Kuznicki, S. M.; Bell, V. A.; Petrovic, I.; Desai, B. T. Small-Pored Crystalline Titanium Molecular Sieve Zeolites and Their Use in Gas Separation Processes. U.S. Patent 6,0686,682, 2000. (8) Das, T. K.; Chandwadkar, A. J.; Budhkar, A. P.; Belhekar, A. A.; Sivasanker, S. Studies on the Synthesis of ETS-10. I. Influence of Synthesis Parameters and Seed Content. Microporous Mater. 1995, 4, 195. (9) Yang, X.; Paillaud, J. L.; van Breukelen, H. F. W. J.; Kessler, H.; Duprey, E. Synthesis of Microporous Titanosilicate ETS-10 with TiF4 or TiO2. Microporous Mesoporous Mater. 2001, 46, 1. (10) Philippou, A.; Anderson, M. W. Structural Investigation of ETS-4. Zeolites 1996, 16, 98. 3033



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(11) Nair, S.; Tsapatsis, M.; Toby, B. H.; Kuznicki, S. M. A Study of Heat-Treatment Induced Framework Contraction in Strontium-ETS-4 by Powder Neutron Diffraction and Vibrational Spectroscopy. J. Am. Chem. Soc. 2001, 123, 12781. (12) Marathe, R. P. Adsorption and Diffusion of Gases in ETS-4. Ph. D. Thesis, National University of Singapore, Singapore, 2006. (13) Marathe, R. P.; Farooq, S.; Srinivasan, M. P. Modeling Gas Adsorption and Transport in Small-pore Titanium Silicate. Langmuir 2005, 21, 4532. (14) Chapman, D. M.; Roe, A. L. Synthesis, Characterization and Crystal chemistry of Microporous Titanium-Silicate Materials. Zeolites 1990, 10, 730. (15) Lechert, H. The Physical Characterization of Zeolites. In Zeolites: Science and Technology; Ribeiro, F. R., Rodrigues, A. E., Rollmann, L. D., Naccache, C., Eds.; Martinus Nijhoff Publshers: The Hague, 1984; pp 151-192. (16) Majumdar, B. Adsorption and Diffusion of Gases in Barium Exchanged Small Pore Titanium Silicate. M.Eng. Thesis, National University of Singapore, Singapore, 2004. (17) Carlson, N. W.; Dranoff, J. S. Competitive Adsorption of Methane and Ethane on 4A Zeolite, Fundamentals of Adsorption. In Fundamentals of Adsorption; Liapis, A. L., Ed.; Engineering Foundation: New York, 1987; pp 129-144. (18) Do, D. D.; Hu, X.; Mayfield, P. L. J. Multicomponent Adsorption of Ethane, n-Butane and n-Pentane in Activated Carbon. Gas Sep. Purif. 1991, 5, 35. (19) Chen, Y. D.; Yang, R. T.; Uawithya, P. Diffusion of Oxygen, Nitrogen and Mixtures in Carbon Molecular Sieves. AIChE J. 1994, 40, 577. (20) Huang, Q.; Farooq, S.; Karimi, I. A. Prediction of Binary Gas Diffusion in Carbon Molecular Sieves at High Pressure. AIChE J. 2004, 50, 351. (21) Bhadra, S. J. Methane-Nitrogen Separation by Pressure Swing Adsorption. M.Eng. Thesis, National University of Singapore, Singapore, 2007. (22) Rao, M. B.; Sircar, S. Thermodynamic Consistency for Binary Gas Adsorption Equilibria. Langmuir 1999, 15, 7258. (23) Habgood, H. W. The Kinetics of Molecular Sieve Action. Sorption of Nitrogen-Methane Mixtures by Linde Molecular Sieve 4A. Can. J. Chem. 1958, 36, 1384. (24) Jayaraman, A.; Hernandez-Maldonado, A. J.; Yang, R. T.; Chinn, D.; Munson, C. L.; Mohr, D. H. Clinoptilolites for nitrogen/ methane separation. Chem. Eng. Sci. 2004, 59, 2407. (25) Mitchell, M. C.; Gallo, M.; Nenoff, T. M. Computer Simulations of Adsorption and Diffusion for Binary Mixtures of Methane and Hydrogen in Titanosilicate. J. Chem. Phys. 2004, 121, 1910. (26) Hu, X. J.; Do, D. D. Multicomponent Adsorption Kinetics of Hydrocarbons onto Activated Carbon: Contribution of Micropore Resistance. Chem. Eng. Sci. 1993, 48, 1317. (27) Huang, Q. Multicomponent Diffusion of Gases in the Micropores of Carbon Molecular Sieves. Ph.D. Thesis, National University of Singapore, Singapore, 2002.

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Adsorption and Diffusion of Methane and Nitrogen in Barium

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