Performance and pore characterization of nanoporous carbon membranes for gas separation

Performance and pore characterization of nanoporous carbon membranes for gas separation

journal of MEMBRANE SCIENCE ELSEVIER Journal of Membrane Science 110 (1996) 109-118 Performance and pore characterization of nanoporous carbon membr...

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journal of MEMBRANE SCIENCE ELSEVIER

Journal of Membrane Science 110 (1996) 109-118

Performance and pore characterization of nanoporous carbon membranes for gas separation M.B. Rao, S. Sircar * Air Products and Chemicals, Inc., 7201 Hamilton Boulevard, Allentown, PA 18195, USA

Received 24 April 1995; revised 31 July 1995; accepted 31 August 1995

Abstract The performance of a novel nanoporous carbon membrane for separation of hydrogen-hydrocarbon gas mixtures is described. The membrane selectively adsorbs hydrocarbons from hydrogen at the high pressure side and the adsorbed molecules then diffuse along the pore walls to the low pressure side. Pressure levels at the high and low pressure sides of the membrane and the type and flow rate of the sweep gas at the low pressure side of the membrane were varied. The effects of these variables on the hydrogen recovery and hydrocarbon rejection by the membrane were investigated. Atomic force microscopy and scanning tunnelling microscopy scans of the membrane surface suggested that the membrane pore diameters were approximately 5 A in diameter. Comparison between pure methane diffusivity through the membrane and those through nanoporous zeolites of various pore openings also suggested that the membrane pores diameters were in the range of 5-6 ~,. A sensitivity analysis indicated that the membranes contained a very narrow distribution of pore sizes. Keywords: Gas separations; Microporous and porous membranes; Selective surface flow; Carbon

I. Introduction A new class of nanoporous carbon membranes for gas separation called selective surface flow ( S S F TM) membranes has been developed by Air Products and Chemicals [ 1 ]. The S S F TM membrane consists of a thin ( 2 - 5 /xm) layer of nanoporous (effective pore diameter in the range of 5 - 6 ,~) carbon supported on a mesoporous (effective pore diameter of 0 . 3 - 1 . 0 / x m ) inert support such as graphite or alumina [ 2 ]. They are produced by coating thin ( 5 - 1 0 / z m ) layers of polyvinylidene chloride latex on the support and then carbonizing the polymer in an inert atmosphere at a temperature of 600-1000°C. The detailed procedure for * Corresponding author. ©Air Products and Chemicals, Inc. Elsevier Science B.V. SSD10376-7388(95)00241-3

making the SSF T M membranes is described elsewhere [1-31. The separation of the components of a gas mixture by the S S F TM membrane takes place by selective adsorption of the more strongly adsorbed components of the mixture on the pore walls of the membrane at the high pressure (pH) side followed by selective surface diffusion of the adsorbed molecules across the membrane to the low pressure (pL) side. Typically, the molecules with larger molecular weight and those with larger polarity and polarizabilities are selectively adsorbed. The adsorbed molecules on the membrane pore wall can also significantly reduce or eliminate the transport of non-selectively adsorbed molecules across the pore by reducing the size of accessible void space through the pore. This hindrance effect introduces a non-adsorptive separation selectivity for the adsorbed

110

M.B. Rao, S. Sircar / Journal of Membrane Science 110 (1996) 109-118

Table 1 Helium diffusivities and estimated pore diameters (Knudsen regime) for carbon plugs and SSFTM membranes Substrate

Porosity (e)

Temperature(K)

Heliumdiffusivity (cmZ/s)

Pore diameter [Eq. (2)] (,~)

Ref.

Carbolac plug Graphon plug Black pearl plug SSFa~ membrane

0.517 0.420 0.430 0.360a

273.1 273.1 273.1 273.1

9.30 × 10- 3 34.4 × 10- 3 12.6× 10 3 0.7×10 s

23.2 85.8 30.6 0.018

[4 ] [5 ] [5] [2]

~Calculated from bulk and chemical densities of the nanoporouscarbon film. components when the pore size is between 2-3 molecular diameters of the adsorbed molecules. The above described mechanisms of transport through the SSF TM membrane were originally demonstrated by Barrer and co-workers [ 4,5 ] by using a compressed cylindrical plug ( 1-2 cm in diameter and 1-2 cm long) of non-porous carbon black. The transport of pure gases and those for the components of binary and multicomponent gas mixtures were measured by imposing a pressure gradient across the plug. The plugs had a porosity (8) of 0.4-0.55 and the effective pore diameters (dp) across the plugs were calculated by measuring non-adsorbing helium flow through them. The helium flux exhibited a V~ dependence of temperature which indicated that flow through the pores was in the Knudsen flow regime (dp> 20 A). Table 1 reports the helium diffusivities (DHe, cm2/s) of these carbon plugs calculated from the measured data as follows:

where D (cm 2/s) is the diffusivity of a pure gas through the pores of the plug. J is the measured flow rate (mol/ s) of a pure gas through the plug under a gas phase concentration gradient ( m o l / c m 3) of AC~[=(PH-PL)/RT] across the membrane. A (cm 2) is the cross sectional area for transport and (cm) is the thickness of the plug. ~- ( > 1) is the tortuosity of the pores within the plug. R is the gas constant and T (K) is the system temperature. For Knudsen flow, dp is related to the Knudsen diffusivity (DK, cm 2/ s) of a pure gas of molecular weight M b y [6]: DK =4.85

×

10-5dp(]/--~)

(2)

where dp is given in ,~ngstrom. It was assumed that the tortuosity was unity (straight holes across the plug),

which gave the smallest possible values for DHe from the measured helium flow rates, and consequently, the smallest possible values of d v. These are reported in Table 1. The minimum pore diameters of the carbon plugs were between 20-85 ,~. The plugs exhibited a certain amount of transport of the pure gases and the components of a gas mixture by surface flow but they also had a significant fraction of the total flow through the void space between the adsorbed molecules (Knudsen mechanism). That reduced the overall selectivity of separation for the gas mixtures. We used the same methodology to calculate the effective pore diameters of the SSF T M membrane. The helium diffusivities were two to three orders of magnitude smaller than those measured through the carbon plugs prepared by Barrer. The corresponding pore diameter calculated by Eq. (2) which assumes Knudsen flow mechanism were much less than 1.0 ,~ (Table 1). That is absurd. Thus, the pores of the SSF TM membrane were in the region ( d p < 10/~) where activated diffusion (even for helium) was the dominant mechanism for transport. This phenomenon was confirmed by comparing pure helium and hydrogen diffusivities at different temperatures through the pores of SSF TM membrane as described by Table 2. Both hydrogen and helium are essentially non-adsorbing gases on carbon surface at the temperature range of the experiTable 2 Helium and hydrogendiffusivities through SSFT M membrane Temperature (K)

256.1 273.1 298.1

Diffusivities( c m Z / s

X

He

H2

0.55 0.72 1.01

3.00 3.59 4.26

105)

DH2/DH~

5.4 5.0 4.2

M.B. Rao, S. Sircar / Journal of Membrane Science 110 (1996) 109-118

ments, yet they both exhibited activated diffusion through the pores of the carbon membrane. The hydrogen (smaller molecule) diffusivities were higher than those for helium through the carbon pores as expected, but the ratio of these diffusivities (DH2/Drte) w e r e in the range of 4-5. For Knudsen flow, the ratio at any temperature should be 1.41. Table 2 further shows that the ratio of diffusivities for hydrogen and helium decreased with increasing temperature which is also contrary to Knudsen mechanism of transport where the ratio should be independent of temperature. The pores of the SSF T M carbon membrane, are therefore, less than 10 .~ in diameter where activated diffusion predominates for all molecules including hydrogen and helium. Consequently, the membrane should separate gas mixtures by the mechanism of selective adsorption and selective surface flow of the components of the mixture only. Selective passage of smaller and less strongly adsorbed components of the gas mixture through the void space between the adsorbed molecules, which reduces the effective selectivity of separation, will not exist.

2. Performance of the SSF T M membrane

Separation of hydrogen-hydrocarbon mixtures by selective adsorption and diffusion of the hydrocarbon molecules through the SSF T M membrane pores was found to be a practical application of the membrane. It can be used to enrich the hydrogen concentration of a gas mixture containing H2 and C1-C4 hydrocarbon mixtures. The enriched hydrogen stream is produced at the high pressure side of the membrane which can be further purified by a conventional pressure swing adsorption (PSA) process [2]. The key advantages of using the SSF T M membrane for such an application are that (a) the low to medium purity hydrogen containing streams (20-60 mol%) at low to medium pressures (20-100 psig) can be enriched, (b) the hydrogen enriched effluent needs to be compressed from the membrane feed gas pressure to the PSA feed pressure (200-300 psig) only, (c) the high permeabilities of the hydrocarbons and their high selectivities over hydrogen result in a low to moderate membrane area requirement, and (d) very high rejections of larger hydrocarbons ( > C 3 ) , which are difficult to desorb from a PSA system, can be achieved. By comparison,

111

Fig. 1. Schematicdiagramof SSFTM membranemodule. most polymeric membranes will require a much higher pressure of operation ( > 200 psig) and they will selectively permeate hydrogen to the low pressure side [7]. That will produce the hydrogen enriched stream at near ambient pressure and the compression duty to feed that gas to the PSA process will be much higher. Polymeric membranes exhibiting selectivity of transport of hydrocarbon molecules over hydrogen do exist but they do not offer good selectivity of separation compared to the SSF T M membranes [ 8 ]. The advantages of the SSF T M membrane can be used to recover H2 from a refinery waste gas (fuel) which typically contains 20-60 mol% H2 in mixtures with C1-C4 hydrocarbons. The separation goal for this application is high hydrogen recovery and hydrocarbon rejections. A membrane module consisting of a plate-and-frame arrangement was used to evaluate the performance of the SSF T M membrane for hydrogen-hydrocarbon separation. Fig. 1 shows a schematic diagram of the module. The SSF T M membranes were produced in the sheet form on a mesoporous (0.7/.~m pore diameter) graphite support for this test. Five sheets of the membrane having a total geometric surface area of 356 c m 2 w e r e mounted in the module. The hydrogen-hydrocarbon feed gas mixture was passed over one side of the membrane sheets at the high pressure. A sweep gas was countercurrently passed through the low pressure side of the membrane. Both high and low pressure gas flow rates, pressures and compositions were measured at the inlet and outlet sides. The pressure drops for these gas streams between the module inlet and outlet were very small ( < 1 psig). A steady state operation was achieved within 30 rain of operation. The entire membrane module was thermostated so that experi-

M.B. Rao, S. Sircar / Journal of Membrane Science 110 (1996) 109-118

112

Table 3 Effect of feeda gas pressure on performanceof SSFT M membrane Pressure (atm) Sweepto feed flow ratio pH

pL

1.35 3.38 4.39 5.11

1.07 1.07 1.07 1.07

0.1 0.1 0.1 0.1

H 2 recovery

Hydrocarbonrejections (%)

High pressure effluentgas compositions(mol%)

CH4

H2

CH4

C2H6

C3Ha

C4Hlo

42.6 49.5 52.1 57.0

21.1 23.2 25.3 26.3

19.5 19.5 17.7 14.5

8.7 6.5 4.5 2.4

8.0 1.3 0.4 0.0

(%)

98.4 80.1 78.5 62.5

C2H6 C3H8 C4Hlo

2.6 9.7 25.0 36.8 23.8 46.8 42.3 68.2

19.3 57.9 73.2 89.4

25.6 91.8 97.6 100.0

aFeed rate = 0.067 mg mol/s. ments could be carried out at a subambient or superambient temperature. The performance of the membrane was evaluated in terms of hydrogen recovery and hydrocarbon rejections. The hydrogen recovery was defined by the fraction of feed gas H2 ( m o l / s ) leaving the module at the high pressure side. The hydrocarbon rejection was defined by the fraction of feed gas hydrocarbon ( m o l / s) leaving the module at the low pressure side. The data reported in this work were obtained by using a feed gas containing 40% H2, 20% CH4, 20% C2H6, 10% C3H 8 and 10% C4Hlo (mol%) at varying feed gas pressures and at a system temperature of 263 K. The feed gas flow rate was fixed at 0.067 mg mol/ s. The sweep gas consisted of pure H2 or CH4 at different pressures. The sweep to feed flow ratio was varied.

2.1. Effect offeed gas pressure Table 3 describes the effect of feed gas pressure (PH) on membrane performance. It was varied between 1.3 to 5.1 atm while maintaining the sweep gas pressure

(pL) at 1.07 atm. The sweep gas (H2) flow rate was 10% of the feed gas flow rate. It may be seen from Table 3 that the membrane performance was significantly improved when p n was increased. The rejections of all hydrocarbons progressively increased as pH was increased. In particular, the rejections of more selectively adsorbed hydrocarbons (ethane, propane and butane) dramatically increased at higher feed gas pressures even though their partial pressure driving forces across the membrane are low. This is due to higher partial pressures of hydrocarbons at the high pressure side of the membrane which increased the specific amounts of hydrocarbon adsorbed at that surface of the membrane and consequently, increased the driving force for their transport across the membrane. The H E recovery decreased with increasing pH for the same reason. Table 3 also shows the high pressure effluent gas compositions. The composition of H2 in the enriched gas increases as pH increases.

2.2. Effect of sweep gas pressure Table 4 shows the results of changing hydrogen sweep gas pressure from 1.07 to 1.48 atm. The sweep

Table 4 Effect of hydrogen sweep gas pressure on performanceof SSFT M membrane Pressure (atm) Sweepto feed flow ratio pH

pL

5.11 5.11

1.07 1.48

0.05 0.05

Feed rate= 0.067 mg mol/s.

H E recovery

Hydrocarbonrejections (%)

High pressure effluentgas compositions(mol%)

CH4 C2H6 C3H8 C4Hlo

H2

CI-14

C2I-I6

C3Hs

C4Hlo

26.9 39.6 22.7 36.7

50.5 49.2

23.9 23.4

19.8 19.2

5.6 6.7

0.16 1.54

(%)

77.1 81.3

60.0 56.0

99.0 89.8

M.B. Rao, S. Sircar / Journal of Membrane Science 110 (1996) 109-118

113

Table 5 Effect of sweepgas type and flowrates on performanceof SSFTM membrane Pressure (atm) Sweep to feed flow ratio p.

H2 recovery (%)

Hydrocarbon rejections (%)

High pressure effluent gas compositions (mol%)

CH4

C2H6

C3H8

C4Hlo

H2

CH4

C2H6

C3H8

C4H10

82.1 78.5 81.5

20.7 23.8 23.0

34.5 46.8 45.9

60.6 73.2 75.2

86.6 97.6 98.3

49.0 52.1 53.0

23.6 25.3 25.0

19.5 17.7 17.6

5.9 4.5 4.0

2.0 0.4 0.28

71.0 70.3 70.1

29.0 29.0 27.7

46.8 51.9 56.4

69.8 76.3 82.4

95.4 97.6 100.0

50.0 51.5 52.9

25.0 26.0 27.3

18.7 17.6 16.5

5.3 4.3 3.3

0.81 0.44 0.0

pL

Hydrogen sweep 4.4 1.07 0.05 4.4 1.07 0.10 4.4 1.07 0.14 Methane sweep 4.4 1.07 0.05 4.4 1.07 0.10 4.4 1.07 0.16 Feed rate = 0.067 mg mol/s.

gas to feed gas flow rates were fixed at 0.05 for these tests. Higher hydrogen sweep gas pressure increases the partial pressures of all components in the low pressure side which reduces the driving force for the transport of all components. Consequently, H2 recovery increases but the rejections of the hydrocarbons decrease. In particular, the concentrations of larger hydrocarbons in the high pressure effluent gas increase substantially. These results show that even a moderate increase in the pressure of the sweep gas diminishes hydrocarbon rejections by several percentage points.

2.3. Effect of sweep gas type and flow rates Several tests were carried out using pure hydrogen and methane as sweep gases as well as by varying the sweep gas inlet flow rates by a factor of three. Table 5 summarizes the results. Increased sweep gas flow rates increased the hydrocarbon rejections for the more selectively adsorbed hydrocarbons (C2-C4) in both cases. The hydrogen recovery and its concentration in the high pressure effluent gas, however, did not change much at higher sweep gas flow rates. The most interesting result was that the hydrocarbon rejections for all components substantially increased while the hydrogen recovery significantly decreased when pure methane was used as the sweep gas. The reason for this result is not clear. One possible explanation is that the specific adsorption capacities of C 2 ~ C 4 hydrocarbons at the low pressure side of the membrane were reduced due to higher gas phase partial pressures of methane which

increased their specific loading differences (hence, driving force for surface diffusion) across the membrane.

2.4. Pore characterization of the SSF T M membrane The hydrogen and helium diffusivities through the SSFT M membrane indicated that the effective pore diameters of the carbon layer are presumably less than 10 ,~. We tried atomic force microscopy (AFM) and scanning tunnelling microscopy (STM) to directly estimate the pore size and distribution as well as the pore density. The AFM scans were obtained by Dr. J.Y. Josefowicz at the School of Chemical Engineering, University of Pennsylvania. The STM scans were obtained by Dr. W. Hoffman of Phillips Laboratory, Edwards Air Force Base. Fig. 2a is an AFM scan of the membrane surface taken over a randomly chosen area of 60 × 60 ,~. It shows ridges and valleyos whose heights and depths extend up to a size of 2 A. They represent the surface roughness of the membrane. Fig. 2b shows a sectional AFM scan of a line across the area of Fig. 2a. The corrugated profile obtained from the line scan again represents surface roughness and it is difficult to identify a pore or its depth. Thus, it was concluded that the AFM imaging could not quantitatively measure the pore size of the SSFT M membrane because the pore diameter was comparable in size with surface roughness. Nevertheless, the size of a depression (assuming

114

M.B. Rao, S. Sircar / Journal of Membrane Science 110 (1996) 109-118

(a)

(b) Fig. 2. Atomicforce microscopeimage of SSb"a~ membrane surface: (a) surface scan; (b) sectional analysis. it to be a pore) indicated by the markers in Fig. 2b was

5.3L Fig. 3a is a STM scan of the membrane surface taken over a randomly chosen area of 100 × 100 ,~. It clearly shows a topology consisting of depths (dark region) and elevations (light region). Fig. 3b is a STM line scan across the area of Fig. 3a. It shows the surface roughness of the membrane as well as clearly identified deep regions (presumably holes). The size of the hole indicated by the markers in Fig. 3b was 4.5 ,~. These direct microscopic measurements did not give conclusive measure of the pore dimensions but they

indicated depressions on the membrane surface whose size was in the 4.5-5.5 ,~ range. 2.5. Pore size calibration by diffusion m e a s u r e m e n t

We constructed a reference plot of methane diffusivity at 295 K through micro- and meso-pores in the size range of 4 - 1 0 000 ~, as shown by Fig. 4. The C H 4 diffusivities through pores having diameters less than 10 A (circles) were obtained from published data for diffusion of CH4 through well calibrated zeolite pore entrances [9,10]. The zeolites included 4A, 5A, sili-

M.B. Rao, S. Sircar / Journal of Membrane Science 110 (1996) 109-118

115

Ca)

L

,

~¢3

j',,,

2~S

5.0

7.5

j.on_M

(b) Fig. 3. Scanningtunnelling microscopeimageof SSFT M membrane:(a) surfacescan; (b) sectionalanalysis. calite and NaX with pore openings of 3.8, 4.2, 5.7 and 7.5 ,~, respectively. The diffusivities of methane through the pores in the diameter range of 20-10 000 ,~ were calculated (circles) by combining contributions due to Knudsen and molecular diffusions [D = DKDM/ ( Dr: + DM) ] according to the model of Scott and Dullien [ 11 ]. The Knudsen diffusivity (DK) was estimated by Eq. (2) and the Chapman-Enskog equation [6] was used to calculate the molecular diffusivity (DM). Molecular diffusion dominates the flow when the pores are large (dp> 1000 A). Knudsen diffusion is the controlling mechanism in the pore diameter range of 20-1000 ,~.

It should be recognized that (a) there are considerable scatter in the published data on diffusivities of methane through zeolite pores, (b) the diffusivities may depend on the extent of dehydration of the zeolite crystals, and (c) the diffusivities are governed not only by the size of the pore of the zeolites but also by the atomic structure of the zeolite crystals and the types and locations of cations present within them. It should also be pointed out that the transition region between Knudsen diffusion and activated diffusion ( 10
M.B. Rao, S. Sircar / Journal of Membrane Science 110 (1996) 109-118

116

1 0° !

i i i iiiil

ii

~i ~i

,o-2 i -4

i

i : i/

!il

/

;iiii -i

~i ! ! ! ! i

i

,

i

E

-8

~

c5 i iili

101°f

ili

10 -12 ~o-~4

F ~,,

]

i,i

iI

i

::

i

i (~ iilii

i

~o

:

1.5

t i'iiiiii iiii i i .....

~,(dp) = F~p) exp(-k * dp) (dp Ip

~,(dp) 1.0

0.5

I \

J

0.0

2

8

alp, A

........ I ', ............. "T '

i i i ~il

............

; . ..i

i

I

10

i

I

i i I I

'

, , II

100 dp,A

I

I

I

I I I I]

, , , ,

1000

I

I

I

It

10000

Fig. 4. Methanediffusivityas a functionof pore diameter. The key point is that the diffusivity of a gas decreases very rapidly with decreasing poore size in the regime of activated diffusion (dp < 10 A). A small change of a few angstroms in the pore diameter can change the gas diffusivity by several orders of magnitude in that region. It should be understood that the use of this reference plot to characterize CH4 diffusion through microporous carbons is an approximation. Methane was chosen as the model gas in Fig. 4 because (a) its spherical shape fixes the relative size of the diffusing molecule with respect to the pore aperture with some certainty, (b) the non-polar nature of methane reduces specific polar interactions with the cationic sites of the zeolite and makes it a weakly adsorbing gas, (c) the relatively slower diffusivities of methane through the zeolites pores make the measurement easier, and (d) there is a l~ge volume of published data for methane-zeolite systems.

We estimated the diffusivity of pure methane through the SSF TM membrane using pressure levels of 1.8 (pH) and 1.0 (pL) atm at 295 K using Eq. (1). The diffusivity value was 1.47 × 10 -5 cm2/s. According to Fig. 4, the pore diameter corresponding to this value of diffusivity is between 5-6 ,~. Given the uncertainty in the estimation of pore size in the activated diffusion regime, our results from both direct microscopic and indirect diffusion measurements show surprising consistency. 2.6. Pore size distribution

In order to estimate the pore size distribution of the SSF T M membrane we empirically fitted the methane diffusivity-pore diameter data of Fig. 4 by an algebraic equation. Two separate equations were needed to

M.B. Rao, S. Sircar / Journal of Membrane Science 110 (1996) 109-118

0.01

:-

i i l - -

T I

! x i i~×

1 0 -4

=: i

-~-6'~

117

~_ ~ k - -

:iiiii~L5 [

/

+_~~

;-i-:

i i

i :

~ ~ ~ ii

~-A I !-~---7-

1 0 -6

03

_ ~°5A

O4

E

.........

:

....

o

1 0 -8

:d

#,A 4.0 4.5 5.0 5.5 5.8 6.0

rj

m

10-1o_ 10

i ! i!~i!i

-12

0.001

0.01

i ~i i!iii c~2

p2

Fig. 5. Overall methane diffusivity as a function of

describe the diffusivities in the low (alp < 12.6 ,~) and high (dp> 12.6 ,~) pore size regions: D ( d p ) = exp [ - 6.31 - 91.82e- O.49dp - - 4 . 1 7 e -3"34dp]

(dp<

12.6,4)

~,A 1.49 1.30 1.06 0.75 0.47

range, A 1.0 - 7.0 1.6 - 7.4 2.3 - 7.7 3.4 - 7.6 4.4 - 7.2 : !

: i

: !

: i

: i

: :

0.1 (O'2//t/,2).

membrane with a heterogeneous pore size distribution is given by: oo

(3a)

b = fD(¢) A(¢) ~ (dp)

(5)

0

DKDM exp[1--3.88e -°26dp

D(dp) = (DK + DM)

--6.10e -°26alp] (dp> 12.6/[)

(3b)

The solid line in Fig. 4 describes the fit of the data by Eq. (3). We assumed that a normalized gamma function described the distribution of pore diameters in the membrane: A ( d p ) = F--~p) e - ~ p ( d P )

( P - 1), ( 0 _< d p < oo)

(4)

where A(dp) is th probability density function. IX(=p/k) and tr( = X/p/k) are the mean and the variance of the distribution, respectively, p and k are parameters of the distribution function. The inset in Fig. 4 gives an example of the function A(dp) calculated for IX= 6.0 ,~ and tr = 0.2 ,~. The overall diffusivity (/9) of a gas through the

Eq. (5) can beintegrated by using Eqs. (3) and (4) for obtaining DCH4, provided that the values for the parameters p and k are chosen (which fixes IXand o-). Fig. 5 shows a family of curves describing/)CH4 as functions of the variable (tr2/ix 2) which were generated using Eq. (5). Each curve corresponds to a given value of the mean pore diameter (IX). It may be seen from Fig. 5 that only a certain combinations of IX and o- values can lead to the experimentally measured /~cn4 value of 1.5 X 10 -5 cm2/s. The tabular inset in Fig. 5 summarizes these results. This analysis shows that the distribution of pore diameters in the membrane must be v e ~ narrow. For example, a mean pore diameter of 5.5 A and a variance of 0.75 (pore diameter range of 3.4-7.6 ,~) will yield the experimental/~CH4 value by the present model. The analysis also shows that the mean pore diameter cannot be larger than 6.0 ,~ in order to obtain the measured methane diffusivity.

118

M.B. Rao, S. Sircar / Journal of Membrane Science 110 (1996) 109-118

T h e a b o v e d e s c r i b e d direct a n d i n d i r e c t m e t h o d s q u a l i t a t i v e l y calibrate the pore sizes o f the S S F T M m e m b r a n e . T h e y s u g g e s t that the m e m b r a n e c o n t a i n s n a n o p o r e s ( m e a n d i a m e t e r o f 5 - 6 .~) w i t h a v e r y narr o w distribution. M o r e q u a n t i t a t i v e m e t h o d s are necessary to c h a r a c t e r i z e t h e s e m e m b r a n e s .

References [ 1] M.B. Rao, S. Sircar and T.C. Golden, Adsorbent Membranes for Gas Separation, U.S. Pat., 5,104,425 (1992). [2] M.B. Rao and S. Sircar, Nanoporous carbon membranes for separation of gas mixtures by selective surface flow, J. Membrane Sci., 85 (1993) 253.

[ 3 ] M.B. Rao and S. Sircar, Nanoporous carbon membrane for gas separation, Gas Sep. Purif., 7 (1993) 279. [4] R. Ash, R.M. Barter and P. Sharma, J. Membrane Sci., 1 (1976) 17. [5] R. Ash, R.W. Baker and R.M. Barrer, Proc. R. Soc., A299 (1967) 434. [6] C.N. Satterfield, Mass Transfer in Heterogeneous Catalysis, M.I.T. Press, Cambridge, MA, 1970. [7] K.J. Doshi, Enhanced Gas Separation Process, U.S. Pat., 4,690,695 (1987). [ 8] L.G. Toy, I. Pinnau, R.W. Baker, Gas Separation Process, U.S. Pat., 5,281,255 (1994). [9] J. Karger and D.M. Ruthven, Diffusion in Zeolites and Other Microporous Solids, Wiley, NJ, 1992. [10] R.M. Barrer, Zeolites and Clay Minerals as Sorbent and Molecular Sieves, Academic Press, London, 1978. [ 11 ] D.S. Scott and F.A.L. Dullien, Diffusion of ideal gases in capillaries and porous solids, AIChE J., 8 (1962) 113.