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Determination of Effective Diffusivities in Commercial Single Pellets: Effect of Water Loading Junhai Guo, Dhananjai B. Shah,* and Orhan Talu Department of Chemical & Biomedical Engineering, CleVeland State UniVersity, CleVeland, Ohio 44115
Single industrial adsorbent pellets of zeolites 5A and 13X were mounted with a polymer capable of withstanding high temperatures. Adsorbents were characterized by mercury-porosimetry and low-temperature N2 adsorption. Isobars of water on these adsorbents at 5 torr were measured using a gravimetric method. Micropores in the pellets were blocked with water loading. Different water loadings in the mounted single pellets were achieved by flowing water-saturated helium through the diffusion cell at different temperatures. Transport through single pellets was studied by measuring steady-state and transient responses in a Wicke-Kallenbach type system. Shift in transient responses was observed as a result of the water loading. Effective diffusivities were calculated from steady-state measurements. A “macropore, micropore, and macropore-micropore-in-series” model was used to estimate the relative contributions from each mode. Effective diffusivities were not affected by water loading in 5A pellets but were affected by water loading in 13X pellets due to increased contribution from the micropores. Introduction Porous materials occur in a great variety both in nature and in industry. Studies on pore structure and pore connectivity in porous materials are both of fundamental and practical importance. In many industrial applications involving adsorption and catalytic processes, the rate of transport in porous adsorbents and catalysts may be the rate controlling step and hence determine the overall efficiency of the process. Therefore, it is a fruitful area of research to study the relationship between the pore structure and the resulting rate of mass transfer. In spite of the fact that pore structure has been extensively studied since the 1960s, a thorough understanding of pore structure and pore connectivity still remains a formidable challenge. Possible explanations for this are the prescence of significant experimental difficulties and complexities in mathematical model development for the study of pore structures. The subject is of considerable fundamental importance due to the industrial application of porous adsorbents in separation processes, catalysts to perform reactions, and potential use of high surface materials for biological applications. The structure of a real pore system is complicated. Pores may be classified by the degree to which they are interconnected to each other. A pore is interconnected if it is accessible from the outside through both ends, and it is isolated if it is not accessible at all. Dead-end pores are connected to the outside through one end only. The degree of pore connectivity in a real pore system is difficult to measure. In addition, pores may have different shapes such as cylindrical, slit, bottle ink, and cage. In the case of industrial adsorbents and catalysts, the pore size distribution may be unimodal or bimodal depending on the type of microparticle and whether a binder has been used in the manufacturing process or not. Pores may also be present as macropores (>500 Å), mesopores (between 20 and 500 Å), and micropores (less than 20 Å) as per the International Union of Pure and Applied Chemistry (IUPAC) classification. The properties of porous materials are strongly influenced by the * To whom correspondence should be addressed. D. B. Shah, Department of Chemical & Biomedical Engineering, Cleveland State University, 2121 Euclid Avenue, Cleveland, Ohio 44115. E-mail:
[email protected]. Tel.: 216-687-3569. Fax: 216-687-9220.
pore structure, namely, the number of pores, pore size distribution, shapes of pores, and degree to which the pores are interconnected. Methods for determining pore structure have been reviewed by Dullien and Batra.1 The methods are classified into two categories: direct and indirect. Direct experimental methods include microscopy and X-ray measurements. These methods determine the physical structure of pores. Indirect methods are based on a combination of experiments and theory. These include capillary theory, fluid flow, and adsorption isotherm and diffusion measurements. This category of methods relies on a postulated mathematical model of pore structure. Most researchers have used indirect methods. Measurement of transport in porous materials is an important experimental approach for investigations of pore structure. Effective diffusivities have been correlated to various simplified mathematical models of pore structure in the literature. In order to explain the differences between observed and calculated diffusivities, tortuosity has been frequently used as an adjustable parameter. It was reported2 that the ratio of the molar fluxes of the two diffusing gases is equal to the inverse ratio of the square root of the molecular weights of the gases. Scott and Dullien3 derived a general equation for the flow of gases in capillaries within the molecular, Knudsen, and transition regions. In a pioneering work, Wakao and Smith4 used pressed Boehmite powder pellets with different porosities to study the diffusion rate at a constant pressure through bidisperse porous media. Pope5 investigated pore structure with gas-phase flow through the solids containing adsorbed molecules. He studied the gasphase diffusion of hydrogen/helium through two well-characterized porous media containing pre-adsorbed sulfur dioxide molecules. The observed permeability depended markedly on the adsorbate concentration. It was postulated that physically adsorbed molecules alter the effective shape of the bottlenecks of pores formed by compressing adsorbent powders. Molecular transport through assemblages of microparticles using an nuclear magnetic resonance (NMR) technique has also been studied.6 A single pellet string reactor was used to measure diffusion coefficients and tortuosity factors for 13 commercial catalysts and supports.7 The setup consisted of a 0.5 m long column
10.1021/ie060747j CCC: $37.00 © 2007 American Chemical Society Published on Web 12/14/2006
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packed with pellets in a string and the ratio of column/particle diameters was in the range of 1.1-1.4. Various theories have been proposed to model pore structure. Some of the models are based on dusty gas concepts.8 Horak and Schneider9 reviewed and compared some of the simplified porous media models such as the continuous media model, parallel bundle model, random macropore-micropore model, and dead-ended pore model for gas diffusion. However, the recent trend in the development of pore network models has been toward formulating more complicated, but realistic, twodimensional and three-dimensional pore network models based on capillary networks.10,11 A more recent review of threedimensional random network models has been provided by Keil.12 More complex two-dimensional and three-dimensional discrete network models which take into consideration pore size distribution and pore connectivity have been used by various researchers to explain mercury intrusion and extrusion,13,14 adsorption and desorption hysteresis,15 coke deposition in catalyst,16 and to determine the connectivity of a porous solid from nitrogen sorption.15,17 Sahimi et al.18 reviewed statistical and continuum models of fluid-solid reactions in porous media. To characterize membranes containing porous materials, the Wicke-Kallenbach technique is one of the more commonly used experimental techniques used to study permeation and diffusion through porous structures.19-23 Most of the literature reports involve self-pressed large pellets for use in a diffusion cell; however, small commercial single pellets have also been used.24 In general, it is more practical to study small size industrial pellets. One problem in using a small pellet is that the industrial pellet must be mounted with a gastight seal and the mounted assembly must be able to withstand high activation/ desorption temperatures. This is a difficult task considering the small size of the pellet and the possible irregular shapes of real adsorbents. If epoxy is used for sealing, it imposes a limit on the maximum temperature that can be used for the measurements and this could be an important factor when activation of the pellet or desorption is to be performed. In one method,25,26 Boehmite powder was compressed in a ring mold into pellets of 1.35 cm in diameter and 0.565 or 0.575 cm in length. Then, the pellet together with the ring mold was put in a diffusion cell and a Teflon O-ring was used to seal the mold. But, a selfmanufactured compressed pellet may have significantly different transport properties from those of a commercial pellet. In an another procedure,27 the mounting of commercial type molecular sieve 13X with a length of 0.35 cm and a cross-sectional area of 1.9 cm2 was reported. A brass disc with drilled holes was used. Samples of catalyst were placed into the holes and the diameters of the holes were adjusted individually for each catalyst. Detailed information about how leak-free sealing was realized was not provided. A small industrial adsorbent is generally around 2 mm in diameter. The beads may not be spherical, and the pellets may not be straight. The above methods, applicable for large pellets, may be difficult to adapt to a small size industrial adsorbent pellet. Multiple mass transfer mechanisms and paths exist across a single pellet. A pellet is likely to possess a bimodal pore size distribution and likely to have macropores, mesopores, and micropores. Transport in micropores of zeolites is governed by “configurational” diffusion whereas that in macropores is governed by molecular diffusion. Transport in mesopores is governed by combination of molecular and Knudsen diffusion. The overall transport process is dependent on the pore structure and the variety of transport mechanisms prevalent in the pores.
Table 1. Measured Physical Properties of Tosoh 5A and Union Carbide 13X Pellets type
Fp (g/cm3)
Fs (g/cm3)
a (%)
BET-N2 (m2/g)
Tosoh 5A pellet Union Carbide 13X pellet
1.1287 1.197
1.6524 1.887
0.317 0.366
538 494
Table 2. Dimensions of Mounted Tosoh 5A and Union Carbide 13X Pellets type
dimension
Tosoh 5A pellet Union Carbide 13X pellet
d ) 1.7 mm, L ) 4.8 mm d ) 1.6 mm, L ) 4.4 mm
Isolation and verification of theses mechanisms and paths experimentally is important in justifying different connectivity models. In this work, a polymer has been used to mount a single small size industrial adsorbent pellet. Water was loaded on the zeolite samples to block access to micropores. Steady-state and transient single-pellet Wicke-Kallenbach experiments were performed at different water loading. Effective diffusivities were calculated from steady state measurements for CH4 and C2H6 in 5A and 13X pellets. A macropore, micropore, and macropore-micropore-in-series model4 was adopted to analyze and explain the experimental observations. Experimental Details Adsorbate-Adsorbent. Methane (CP), ethane (CP), and helium (zero grade) were used as proble molecules. The 5A pellets were supplied by Tosoh and the 13X pellets (LOT 945389070005) came from Union Carbide. Both adsorbents were characterized by Micromeritics Mercury PoreSizer 9320 and ASAP 2010 N2 adsorption equipment. Measured bulk and solid density, porosity, and BET surface areas are listed in Table 1. Both 5A and 13X pellets were of bimodal pore size distribution. Typical dimensions of the 5A and 13X pellets are given in Table 2. Isotherms and Isobars. Isotherms of CH4 and C2H6 in the Tosoh 5A pellet and the Union Carbide 13X pellet at 30 °C were measured using a Cahn 1000 gravimetric balance. These are shown in Figure 1 a and b, respectively. The isotherms are regressed using the Langmuir model, and the regressed parameters are listed in Table 3. Isobars of water at 0 °C in 5A and 13X were also measured. The samples were activated at 320 °C overnight and then exposed to water vapor from a metal bottle which was surrounded by ice. A water vapor pressure of about 5 torr was easily achieved by controlling the temperature of water to 0 °C. Isobars in the range of 20-260 °C on the Tosoh 5A and Union Carbide 13X were measured. The results are given in Figure 2. The measured isobars are consistent with measured BET surface areas for 5A and 13X samples. Wicke-Kallenbach System. We have used a similar configuration as that reported in the literature with a few modifications for the study of a small size industrial adsorbent pellet. Figure 3 shows the schematics of the experimental setup. Figure 4 shows a detailed configuration of a diffusion cell. A sweeping side stream is split into the flame ionization detector (FID) directly so that the transient process can be captured. The FID analog signal is converted by an ADC-16 analog-to-digital converter, fed into the computer, and then logged. The system pressure is controlled by a back pressure controller (BPC) and monitored by a low-range pressure gauge. The pressure balance between the two sides of the diffusion cell is achieved by tying the feed stream and sweeping stream at the inlet of the BPC, and same length and symmetric tubing was used for both sides.
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Figure 3. Schematics of a Wicke-Kallenbach system.
Figure 4. Schematics of the diffusion cell.
Figure 1. Isotherm of CH4 and C2H6 at 30 °C of (a) a Tosoh 5A pellet and (b) a Union Carbide 13X pellet.
Figure 2. Isobar of water on Tosoh SA and Union Carbide 13X pellets at 5 torr.
The tubing layout is designed carefully so that back diffusion and time lag is minimized. An eight-way valve is used to accomplish the switching. The temperature is controlled by the
gas chromatography (GC) oven. Copper coil is used to heat up and cool down both the mixture and sweeping gas streams. The temperatures of the two sides of the diffusion cell are controlled by the GC oven within (0.5 °C and monitored by thermocouples. By fixing the system pressure and the extent to which the valve NV1 is open, the flow rate to the FID is fixed even though the actual flow rate to the FID is not known. The diffusion cell is quite similar to that of the single-crystal membrane system used by Sun et al.,28 but with helium flowing around the diffusion cell to protect the Kalrez O-ring and polymer washer from being oxidized at high temperature. The diffusion cell is designed carefully to minimize film resistance. A step change instead of a pulse input was used since a real industrial pellet has a small cross-sectional area and a pulse input may give a weak response. Also, strong adsorption may widen the pulse response significantly which may make accurate measurements difficult. Pellet Mounting. The high-temperature polymer was supplied by Air Product and Chemicals. Pellet mounting was accomplished in a series of steps. In the first step, a polymer washer was manufactured. The polymer solution was poured into a clean beaker to a height of about 3 mm and covered with a thin paper in order to control its evaporation rate. The polymer was allowed to dry for about 10 d. The resulting polymer membrane was peeled from the beaker, and polymer washers of about 1.2 cm in diameter were cut from this large membrane. The washer had very good mechanical properties. Blank polymer washers were tested for leaks at 250 °C, and no leaks were observed. In the second step, a hole was drilled in the polymer washer to accommodate the pellet to be mounted. The washer was then cleaned and dried. In the third step, the pellet to be mounted was wrapped by a layer of polymer solution and dried immediately for about 2 min. A few more layers were applied to guarantee gastight sealing. In the last step, the wrapped pellet was glued to the washer with the polymer solution and was dried in the beaker for about 12 h. The mounted pellet was then polished on one side by sand paper and leak-tested in the diffusion cell using methane as the probe molecule. The
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Figure 6. Scanning electron micrograph of polymer and Tosoh 5A boundary.
adsorption isobars were applicable. In this way, we could control the water loading on the adsorbent and thus the extent of micropore blockage by water adsorption. At the same time, the GC oven was set to a temperature that corresponded to the desired water loading as determined from the measured isobars. The bubbling procedure was continued for 15 h to ensure that equilibrium was reached. The oven temperature was then set back to the experimental temperature of 30 °C, and helium flow was bypassed from the water bubbler. Due to strong water adsorption, it was assumed that water would remain adsorbed after lowering the oven temperature. Before each experiment, the pellet was purged using helium flow for about half an hour to remove water vapor trapped in the macropores. An adsorption step was started by switching the eight-way valve from the load to the “inject” position so that the sweeping side was swept by helium and the feed side by the helium and adsorbate mixture. After steady state was reached, a desorption step was commenced by switching the eight-way valve back to the load position. It took at least 6 h at 200 °C with helium purge flow to remove adsorbed water. Data Analysis Figure 5. Comparison of two mounted and randomly picked Union Carbide 13X pellets. (a) Steady-state. (b) Transient.
Steady-state apparent effective diffusivity was calculated by the following formula:
temperature was raised at a rate of 2 °C/min to 250 °C and held there for a couple of hours. Then, the oven was allowed to cool down to room temperature and a leak test was performed. If no leak was detected, then the other side of the pellet was polished. The dimensions of mounted pellets used in this work are listed in Table 2. Figure 5a and b show the comparison of steady-state and transient responses of two randomly picked Union Carbide 13X pellets with approximately identical dimensions. The reproducibility of results is quite good. From Figure 5a, it is reasonable to conclude that gastight sealing has been achieved since if there were pinholes in the mounting layer, the transient breakthrough would be immediate. Figure 6 shows a scanning electron micrograph depicting the boundary between the polymer and the Tosoh 5A pellet. It can be seen that the polymer basically wraps the pellet and a clear boundary exists between the two materials. Procedure. A mounted pellet or bead was activated at 200 °C for about 6 h with the eight-way valve in the “load” position so that there was helium flow on both sides of the diffusion cell. After activation, the helium stream was switched to bubble through deionized and distilled water maintained at 0 °C using a fine bubbler. By bubbling through 0 °C water, we achieved a vapor pressure of 5 torr and ensured that the measured water
QSTP sweepLyA2
Deff )
A(yA1
(RTP ) P - y )( ) RT A2
STP
(1)
exp
where A is the total cross-sectional area (pore plus solid). Here, possible mass transfer mechanisms are lumped in Deff. In order to estimate the contribution from different mechanisms, we adapted a “macropore, micropore, and macropore-microporein-series model”4 to the case of zeolite material with strong adsorption. The original model was based on probability analysis of cross-rejoined microparticles and was used to predict the diffusion rate at constant pressure through bidisperse porous media using a pressed Boehmite powder pellet with different porosities. The total flux, NAT is assumed to comprise of three contributions as given by eq 2
NAT ) a2NA1 + (1 - a)2NA2 + 2a(1 - a)NA3 V V V (mechanism 1) (mechanism 2) (mechanism 3)
(2)
Here, mechanism 1 stands for the flux contribution from macropores formed by cross-rejoining of the two microparticles
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with geometric probability a2. Mechanism 2 stands for the contribution from microparticles with geometry probability (1 - a)2, and mechanism 3 stands for the contribution from macropores-micropores in series with geometric probability of 1 - a2 - (I - a)2. These probability factors are based on the geometrical representation of the pore structure by Wakao and Smith4 (Figure 1 in their paper). A Wicke-Kallenbach system features counterdiffusion.1,3,29 For mechanism 1,
NA1 ) where Da )
dya P Da RT dx
(3)
1 1 - Rya 1 + DAB DKA
(4)
For mechanism 2, we have
(
)
dµA pA RT dpA ) -BA nAFA + i dx RT pA dx nA dyA P with D0 ) BART (5) ) - D0 FRT + i RT pA dx
NA2 ) -BAqA
(
)
If we assume a Langmuir isotherm, then we have
NA2 ) -
(
)
n∞Ab dyA P FRT + i D0 RT 1 + bPyA dx
We can further define
(
D i ) D0
(6)
)
n∞Ab FRT + i 1 + bPyA
(7)
and ignore the presence of gas molecules in micropores. For mechanism 3,
NA3 ) -
( )
dyA P 2 1 dx RT 1 + Da Di
(8)
( ) ( )
Integrating the above equations, we get
DAB a DABP DKA ln NAT ) DAB L RRT 1 - RyA1 + DKA
( )
1 - RyA2 +
2
-
(
)
(1 - a)2 1 + bPyA2 (D0n∞AF) ln L 1 + bPyA1
( ) ( )
DABP (D0n∞AF) 4a(1 - a) RRT × L DABP ∞ - (D0nAR) RRT
(
( (
DAB DAB 1 + bPyA2 + DKA D0 n∞bFRT A ln DAB DAB 1 + bPyA1 1 - RyA1 + + DKA D0 n∞bFRT 1 - RyA2 +
A
)
) )
DN ) DNI + DN2 + DN3
( ( ))
where
DAB DAB DKA DN1 ) a2 ln DAB R(yA1 - yA2) 1 - RyA1 + DKA (1 - a)2 RT 1 + bPyA2 DN2 ) , and (D0n∞AF) ln P 1 + bPyA1 (yA1 - yA2)
(
DN3 ) -
)
((
1 - RyA2 +
)
(D0n∞AF) × R(yA1 - yA2) DABP ∞ - (D0nAR) RRT DAB DAB 1 + bPyA2 1 - RyA2 + + DKA D0 n∞bFRT A ln DAB DAB 1 + bPyA1 1 - RyA1 + + DKA D0 n∞bFRT A
4a(1 - a)DAB
(
)
( (
If we define a lumped total Fickcian diffusivity DN, we have
(10)
What we calculated from eq 1 is actually the diffusivity defined by eq 10 which is a lumped property and is obviously concentration dependent. The concentration dependency is generally insignificant especially in the low concentration region. In the literature, when pulse instead of step input has been used, Deff is usually regarded as a constant. Equation 10 is completely general but does contain many parameters. In order to see the trends of different contributions, eq 10 was used to calculate the overall diffusivity DN and the individual diffusivities DN1, DN2, and DN3. Figure 7 a and b show typical results with R ) -1.0, D0 ) 1.0 × 10-8 m2/s, b ) 9.757 × 10-4 1/torr, n∞A ) 30.51 mg/g, F ) 1088.8 kg/m3, T ) 303.13 K, P ) 1200 mbar, a ) 0.3656, yA2 ) 0, DAB ) 0.59 cm2/s, and DKA ) 0.51 cm2/ s. This plot predicts that total effective diffusivity decreases as feed side composition increases and blocking of the micropore path will cause a slight shift in total effective diffusivity. For the assumed values of the parameters, it is clear from the figure that approximately 88% of the total overall transport is through macropores and the other two mechanisms only contribute about 12% to the overall transport. The above equation is not easily amenable to estimating the relative contributions of the individual mechanisms to the overall transport. However, a more simplified expression may be derived if several assumptions are made to estimate contributions of different terms. If we assume tortuosity is equal to 1/a, the first term on the right-hand side of eq 10 is actually the effective macropore diffusivity Da,eff. Assume further that Da . Di and that Da and Di are constant, i.e., that the feed stream is dilute and that the adsorption equilibrium isotherm may be expressed by Henry’s law, nA ) KcA, where both nA and cA are expressed in moles per cubic centimeter and K is the dimensionless adsorption equilibrium constant. The Langmuir isotherm equation expressed in terms of nA and pA reduces to Henry’s law in the limit as b f 0, and in that case, K may be expressed as n∞AbRT. Equation 10 then gets simplified to
Deff ) Da,eff + KD0(1 + 2a - 3a2) (9)
)
) )
(11)
We can simply regard Deff as the total effective diffusivity calculated from eq 1, Da,eff as the measured effective diffusivity when the micropore path is completely blocked by water, and the last term in eq 11 as a contribution from the micropore and macropore-micropore-in-series paths. Equation 11 allows us
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Figure 7. Typical plot of contributions of different mass transfer mechanisms to DN in the adapted Wakao and Smith model.
to calculate in a simplified manner the relative contribution that each mechanism makes to the overall transport. Results and Discussion Figure 8 a and b show the effective diffusivities calculated from steady-state responses of the Wicke-Kallenbach system for a Tosoh 5A and a Union carbide 13X pellet. As predicted by eq 10, the effective diffusivities of methane and ethane decrease for both pellets with increasing mole fractions on the feed side. The values of diffusivities for methane and ethane in the Tosoh 5A pellet are about 3-3.5 × 10-6 and 1.4-1.7 × 10-6 m2/s whereas those in the 13X pellet are 3-3.5 × 10-6 and 1.5-2 × 10-6 m2/s, respectively. An interesting result from Figure 8 is that the extent of water loading has no perceptible effect on the magnitude of effective diffusivities for the 5A pellet. The effective diffusivities for the dry pellet and the 20% water-loaded pellet are about the same. However, increasing the water loading decreases the effective diffusivities slightly for 0%, 5%, and 10% water loading but noticeably for 20% water loading for the 13X pellet. An approximately 20% difference between the cases with the 20% water-loaded and the 0% water-loaded pellet is observed for the C2H6-helium system, and around a 10% difference is observed for the CH4-helium system. It appears that increasing the water loading on the 13X pellets decreases the effective diffusivities even though the effective diffusivities for the 0%, 5%, and 10% water-loaded 13X pellets are closely bunched together and the minor differences between these three different samples may be within the margin of experimental errors. However, the differences in effective diffusivities between the 0% water-loaded and 20% water-loaded pellet are significant. Repeated experiments performed with the same operating conditions confirmed that this observed difference in 13X was real and not due to experimental errors (estimated to be < (5%).
Figure 8. Effect of water loading on the steady-state Deff value at 30 °C and 1200 mbar. (a) CH4-He and C2H6-He in a Tosoh 5A pellet. (b) CH4He and C2H6-He in a Union Carbide 13X pellet.
The decreasing values of diffusivities with water loading may be attributed to the reduction of the cross-sectional area due to water condensation. However, this was ruled out because the 5A pellets did not show similar results and mercury penetration curves confirmed that pore sizes are not in the capillary force region (20-500 Å). A more reasonable explanation is that the mass transfer contribution from the micropores is much more significant for the 13X pellet than for the 5A pellet. Equation 11 shows that the magnitude of the micropore-related contribution depends on both the adsorption equilibrium constant and the micropore diffusivities. Table 3 lists the adsorption constants derived from our measurements and micropore diffusivities reported in the literature. Roughly, the adsorption constants K for 5A for both methane and ethane are approximately twice those for 13X, but the micropore diffusivities in 5A are smaller for methane by about a factor of 2 and for ethane by an order of magnitude compared to those in 13X. The estimated percent micropore related contributions calculated from eq 11 are given in the last row of Table 3. The contribution from micropores is a small fraction of the total transport for the 5A pellet. This explanation is consistent with the fact that water loading does not appear to affect effective diffusivities in 5A. The micropore contribution in the case of 13X for methane is much lower (1.6%), but for ethane, it is much higher (>30%). For ethane, the micropore contribution in 13X is 5 times higher than that
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Table 3. Estimation of Micropore-Related Contribution to Total Steady-State Effective Diffusivity at 30 °C and 1200 mbar Tosoh 5A
qs, mg/g b, 1/torr K, dimless D0, m2/s KD0, m2/s (1 + 2a - 3a2)KD0, m2/s Deff, m2/s % from micropores
Union Carbide 13X
CH4
C2H6
CH4
C2H6
30.51 9.757 × 10-4 40 10-9 a 4 × 10-8 6.1 × 10-8
78.61 1.012 × 10-2 566 10-10 b 5.7 × 10-8 8.7 × 10-8
58.77 1.88 × 10-4 16 2 × 10-9 c 3.2 × 10-8 5.1 × 10-8
100.2 3.81 × 10-3 288 10-9 c 2.9 × 10-7 4.6 × 10-7
3.3 × 10-6 1.85
1.5 × 10x-6 5.8
3.2 × 10-6 1.6
1.5 × 10-6 30.7
a Reference 30, p 391. b Reference 30, p 392; value extrapolated to 298 K. c Reference 30, p 436; values estimated from Figure 13.5.
in 5A and hence represents a much larger fraction of the overall transport rate. The experimental results for the C2H6-13X system are consistent with a higher percentage contribution from the micropores. However, for the CH4-13X system, the estimated micropore contribution is only 1.6%. Under these conditions, water loading on 13X should not affect the effective diffusivity of methane in 13X, but it does seem to decrease with water loading. One reason for this underestimation of micropore contribution may be the uncertainty associated with estimating micropore diffusivities of methane in 13X. Methane, being a small molecule and 13X being a large pore zeolite, diffuses much more rapidly, and as a result, many of the macroscopic methods of measuring diffusivities do not work well for this system. The estimated diffusivities of methane in 13X have been based on values determined from microscopic methods.30 It was hoped that by using a water loading of 20%, all access to the micropores would be blocked. Then, we could approximately regard the measured effective diffusivity at water loadings of 20% and 0% as the macropore effective diffusivity and the total effective diffusivity, respectively. This statement is supported by the transient responses for C2H6 shown in Figure 9 a and b for the 5A and 13X pellets, respectively. Figure 9a and b shows almost an instantaneous breakthrough for the pellets that are loaded with water. Since, in that case, the micropores are completely blocked due to water loading, the micropore transport does not contribute to the overall mass transfer. As the water loading is reduced, a greater and greater fraction of micropores become available for diffusion and the response curves take some time to reach steady state with the unloaded pellet showing 25 min for 5A and 8 min for 13x to reach steady-state values. The reduced time needed to achieve steady state for the 13X pellet is also due to the larger sized windows in 13X and the resulting higher micropore diffusivities. From Table 3, it is easy to see that the estimated value of the micropore-related contribution for ethane in 13X is basically consistent with the experimental measurements.
Figure 9. Effect of water loading on transient responses at 30 °C, 1200 mbar, and a feed side volume fraction of 0.1. (a) C2H6-He in a Tosoh 5A pellet. (b) C2H6-He in a Union Carbide 13X pellet.
than in 5A. A macropore, micropore, and macropore-micropore-in-series model was reasonably successful in explaining the experimental observations. Acknowledgment We gratefully acknowledge the financial support by EFFRD, Research Council of Cleveland State University, and Air Products and Chemicals. We are also thankful to Air Product and Chemicals for providing the high-temperature polymer. Nomenclature
Conclusions To study the effect of water loading on effective diffusivities in bimodal pore structures, small size industrial adsorbent pellets were successfully mounted to fabricate single-pellet membranes. The membranes were placed in a diffusion cell and a WickeKallenbach technique was successfully used to determine the effect of water loading on the effective diffusivities of methane and ethane in 5A and 13X pellets. Transient responses were shifted due to water loading. The relative contribution of transport through micropores for more strongly adsorbed ethane was significant for 13X pellets and insignificant for 5A pellets. This is due to significantly higher micropore diffusivities in 13X
A ) pellet section area (solid plus void), m2 b ) Langmuir adsorption constant of component A, l/torr cA ) gas-phase concentration, mol/cc Deff ) total effective diffusivity, m2/s D0 ) corrected micropore diffusivity, m2/s Da ) macropore diffusivity, m2/s Dj ) micropore diffusivity, m2/s DN ) total integral effective diffusivity, m2/s DN1 ) integral macropore path diffusivity, m2/s DN2 ) integral micrpore path diffusivity, m2/s DN3 ) integral macropore-micropore-in-series diffusivity, m2/s Da,eff ) effective macropore diffusivity, m2/s
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DAB ) free molecular diffusivity, cm2/s DKA ) knudsen diffusivity, cm2/s Deff ) total effective diffusivity of pellet, m2/s d ) pellet diameter, mm K ) dimensionless adsorption equilibrium constant or Henry constant L ) pellet length, m nA ) adsorbed amount, mol/kg or mol/cc n∞A ) saturated adsorption amount, mol/kg or mol/cc NAT ) total flux, mol/s‚m2 NAI ) flux by macropore path, mol/s‚m2 NA2 ) flux by micropore path, mol/s‚m2 NA3 ) flux by macropore-micropore in series path, mol/s‚m2 P ) pressure, Pa pA ) partial pressure of component A qS ) saturated adsorption amount, mg/g dry sample QSTP sweep ) flow rate of sweep side stream at standard temperature and pressure (STP), m3/s T ) temperature, K x ) pellet length direction, m yA ) volume fraction of component A yA1 ) feed side volume fraction of component A yA2 ) steady-state sweeping side volume fraction of component A a ) 1 + flux ratio of counterdiffused species F, FP ) pellet density, g/cm3 Fs ) solid density, g/cm3 a ) macropore porosity i ) micropore porosity µA ) chemical potential of component A Literature Cited (1) Dullien, F. A. L.; Batra, V. K. Determination of the Structure of Porous Media. Ind. Eng. Chem. 1970, 62, 25. (2) Hoogschagen, J. Diffusion in Porous Catalysts and Adsorbents. Ind. Eng. Chem. 1955, 47, 906. (3) Scott, D. S.; Dullien, F. A. L. Diffusion of Ideal Gases in Capillaries and Porous Solids. AIChE J. 1962, 8, 113. (4) Wakao, N.; Smith, J. M. Diffusion in Catalyst Pellets. Chem. Eng. Sci. 1962, 17, 825. (5) Pope, C. G. Pore Structure Investigation using Gas Phase Flow through Microporous Solids Containing Adsorbed Molecules. Faraday Sci. Trans. 1968, 64, 566. (6) Karger, J.; Kocirik, M.; Zikanova, A. Molecular Transport through Assemblages of Microporous Particles. J. Colloid Interface Sci. 1981, 84, 240. (7) Sharma, R. K.; Cresswell, D. L.; Esmond, J. N. Effective Diffusion Coefficients and Tortuosity Factors for Commercial Catalysts. Ind. Eng. Chem. Res. 1991, 30, 1429. (8) Mason, E. A.; Malinauskas, A. P. Gas Transport in Porous Media: The Dusty-Gas Model; Elsevier: Amsterdam, 1983. (9) Horak, Z.; Schneider, P. Comparison of Some Models of Porous Media for Gas Diffusion. Chem. Eng. J. 1971, 2, 26.
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ReceiVed for reView June 12, 2006 ReVised manuscript receiVed October 23, 2006 Accepted October 30, 2006 IE060747J
