CO2 permeation through a silicalite-1 composite membrane

Journal of Membrane Science 375 (2011) 313–322

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H2 /CO2 permeation through a silicalite-1 composite membrane Sang Kompiang Wirawan a,b,c , Derek Creaser a,∗ , Jonas Lindmark b , Jonas Hedlund b , I. Made Bendiyasa c , Wahyudi Budi Sediawan c a b c

Chemical Reaction Engineering, Chalmers University of Technology, 412 96 Göteborg, Sweden Division of Chemical Engineering, Luleå University of Technology, 971 87 Luleå, Sweden Department of Chemical Engineering, Faculty of Engineering, Gadjah Mada University, 55281 Yogyakarta, Indonesia

a r t i c l e

i n f o

Article history: Received 17 September 2010 Received in revised form 23 March 2011 Accepted 30 March 2011 Available online 7 April 2011 Keywords: Zeolite composite membrane H2 /CO2 permeation Surface diffusion Gas translational diffusion Membrane defects

a b s t r a c t Single and binary H2 /CO2 gas permeation was studied through a silicalite-1 composite membrane consisting of a thin zeolite film (<1 ␮m) supported on ␣-alumina. The temperature range for permeation measurements was 25–300 ◦ C. To determine the quality of the membrane, i.e. the quantity and size of defects, n-hexane/helium permporometry measurements were performed. In general, single component fluxes decreased with increasing temperature whereas binary component fluxes showed a maximum value followed by a continuous decrease. A mass transport model that takes into account the surface diffusion and gas translational diffusion in the zeolite pores, Knudsen diffusion in defects, as well as viscous flow and Knudsen diffusion in the support material was developed to simulate the single and binary gas permeation measurements. Simulation results show that the surface diffusion was the dominant mass transport mechanism in the membrane. In addition, the transport resistance of the support material was not negligible and it was found to influence the permeation selectivity. The model adequately described the experimental results for both single and binary permeation. The model predictions indicated that a CO2 /H2 separation factor exceeding 9.8 and a CO2 flux exceeding 4 mol/(m2 s) could be obtained at 0 ◦ C and a feed pressure of 10 bar and atmospheric permeate pressure. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Fundamental studies on single and multi-component gas transport in MFI zeolite membranes, especially transport through silicalite-1 zeolite membranes, have been presented and a few selected examples are given in the reference list [1–9]. Often in these modeling studies, only the transport resistance posed by the zeolite film part of the membrane is considered, whereas the resistance of the porous support material on which the zeolite film is grown, is not taken into account. Another common assumption made in most studies is that the membrane is defect free. The presence of defects in the membrane and their contribution to the overall gas transport is not quantitatively considered. However, for a membrane with a thin zeolite film, the support resistance is not negligible and it may influence the flux and selectivity. In addition, the presence of even a small amount of defects may also affect the membrane separation performance. There is still a lack of attention to these issues in most of the reported studies. However, there are a few reports on modeling of mass transport in MFI membranes which include the support

∗ Corresponding author. Tel.: +46 31 7723023; fax: +46 31 7723035. E-mail address: [email protected] (D. Creaser). 0376-7388/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2011.03.061

resistance and defect contribution. A binary diffusion model was applied for the porous support [10,11]. The influence of the support was calculated with the dusty gas [11] and pseudo-binary diffusion [10] models. In [12], the authors discussed a method to estimate the contribution of transport through defects in the overall membrane transport. Studies of H2 /CO2 single or binary permeation in MFI zeolite membranes via experiment or model predictions have been reported [6,9,14]. It is well known that at low temperature, the membrane is CO2 permselective due to the stronger adsorption of CO2 , whereas at higher temperature, it is H2 permselective. Most of the zeolite membrane studies reported previously have used a relatively thick zeolite film, i.e. much thicker than 1 ␮m, and typically in the range of 5–40 ␮m. A composite membrane with a thin zeolite film may be desirable because it provides a higher flux per membrane area, however the support transport resistance is less likely to be negligible and it may even significantly influence the membrane performance. Thus the use of an ultra-thin zeolite film (<1 ␮m) in a composite membrane is another unique aspect of the current study. An early fundamental theoretical study of diffusion in micropores was presented by Xiao and Wei [15]. Diffusion in the microporous media was described in terms of adsorption and surface diffusion; mass transport took place in the adsorbed phase

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and was pictured as molecules hopping between fixed adsorption sites. For the mass transport, a diffusion activation energy had to be overcome. The hopping model, called the solid vibration model, was derived and an activated gaseous diffusion model called the gas translational diffusion model was obtained. Another commonly used model to describe the permeation through a zeolite membrane is the generalized Maxwell-Stefan (GMS) theory, applied for multicomponent systems [16]. Based on their model, verified by experimental data, Bakker et al. [9] found that the temperature dependence of the steady state single component fluxes through a silicalite-1 membrane could be described only if two diffusion mechanisms are taken into account. For high occupancies, the mass transport could be described by equilibrium adsorption followed by surface diffusion, and for low occupancies, mass transport could be described by the activated gaseous diffusion. They also found that with increasing temperature, the dominant mass transport mechanism shifts from the surface diffusion regime to the activated gaseous diffusion regime. Our group has developed a model [13] for single gas permeation accounting for mass transport in zeolite pores, defects and substrate and the model developed in the present work is an extension of that model to binary mixtures. The present work considers single component and binary H2 /CO2 permeation through a composite silicalite-1/alumina membrane. The composite membrane consisted of an ultra-thin silicalite-1 film (<1 ␮m thick) grown on a graded ␣-alumina support. The differences in the adsorption and mobility between H2 and CO2 in silicalite-1 means that the permselectivity should depend strongly on temperature which is an interesting aspect of this system to simulate in a modeling study. The parameters needed to account for the support resistance and transport through defects were determined by independent experiments. In the proposed model, the following transport mechanisms were included; surface diffusion and gas translational diffusion in zeolite pores, Knudsen diffusion in defects, as well as viscous flow and Knudsen diffusion in the support material. 2. Experimental methods 2.1. Membrane preparation Silicalite-1 membranes with a circa 500 nm thick zeolite film were prepared as reported elsewhere [17]. The supports were discs of porous ␣-alumina with a diameter of 25 mm (Inocermic GmbH, Germany). The top layer, denoted S1, with a pore size of 100 nm was 30 ␮m thick. This layer is supported by layer S2, which is 3 mm thick with a pore size of 3 ␮m. The supports were seeded with colloidal silicalite-1 crystals (50 nm). A film was grown by hydrothermal synthesis on the seeded surface of the masked support. The membranes were calcined at 500 ◦ C with a heating and cooling rate of 0.2 ◦ C/min after the synthesis. In order to more accurately determine the membrane thickness, SEM analysis of the membrane cross-section was carried out with a scanning electron microscope (FEI Magellan 400 field emission XHR-SEM). 2.2. Permporometry measurements The zeolite membranes were characterized by n-hexane permporometry as reported previously [17]. Permporometry was carried out in a stainless steel cell which had two compartments separated by the membrane. The membrane was dried at 300 ◦ C overnight in a flow of dry helium then cooled to room temperature. The helium permeance at room temperature was recorded as the relative partial pressure of n-hexane was successively increased. The relative pressure of n-hexane was set to approximately 0.01, 0.025, 0.25, 0.85 and 1.0. The permeance of helium was measured

with a total pressure difference of 1 bar with the permeate side maintained at atmospheric pressure. The permeance was measured using a flow meter connected after a condenser and a column with activated carbon, which removed the n-hexane. 2.3. Gas permeation measurements Gas permeation measurements through zeolite membranes are generally performed by either concentration gradient or total pressure drop methods [18]. In the concentration gradient method, gases are supplied to both sides of the membrane. An inert sweep gas (usually He or Ar) is fed at the permeate side. In this method the permeation is due to concentration gradients whereas the total pressure is equal on both sides of the membrane. In the pressure drop method an absolute pressure difference is applied over the membrane. It has been observed that in the concentration gradient method, the sweep gas can diffuse from the permeate side to the feed side, thus affecting the permeation of the species of interest and complicating the evaluation of results [19]. In this present work, the pressure drop method was used for single and binary gas permeation experiments. The permeate side total pressure was maintained at 1 bar for both single and binary permeation experiments. The temperature range used was 25–300 ◦ C. For the single gas permeation, the applied membrane pressure difference (P) was 0.3–0.8 bar. For the binary H2 /CO2 gas permeation, the total feed pressure was set at 1.4 bar with the feed gas compositions of 50/50 and 70/30 (H2 /CO2 feed molar ratio). The feed gas mixture was supplied by two mass flow controllers with a total flow rate of 1000 ml/min (ambient conditions). The membranes were kept in the same cell as used for permporometry experiments and the cell was placed in a temperature controlled electric heater. The temperature close to the membrane was monitored with a thermocouple inserted inside the cell. For the single gas permeation, the permeate flux for a given temperature was measured with a digital volumetric flow measurement device. For the binary permeation measurements, the setup was slightly changed. In addition to the volumetric flow rate measurement, the permeating gas was analyzed by a gas chromatograph to determine its composition. Before the permeation measurements, both the feed and the permeate sides were swept with helium while heating the membrane up to 300 ◦ C by using a 1 ◦ C/min temperature ramp. 3. Mathematical modeling A model for mass transport was developed to simulate the single and binary gas permeation through the silicalite-1 membrane. The following transport mechanisms are included in the model; surface diffusion and gas translational diffusion in zeolite crystals, Knudsen diffusion in defects, as well as viscous flow and Knudsen diffusion in the support material. 3.1. Transport in the support material Fig. 1 shows the structure of the silicalite-1 composite membrane with a schematic drawing. The top layer ␦ is the zeolite film. The ␣-alumina support consisted of layer S1, 30 ␮m thick (␦S1 ) with 100 nm pores, and layer S2, 3 mm thick (␦S2 ) with 3 ␮m pores. Transport in layer S1 was modeled by a combination of Knudsen diffusion and Poiseuille flow. However, Poiseuille flow was assumed to be the only transport mechanism of importance in layer S2 [13]. This is due to the fact that the gases such as H2 and CO2 under the relevant experimental conditions have a mean free path similar to the pore size of layer S1, while the pores in layer S2 are much larger than the mean free paths.

S.K. Wirawan et al. / Journal of Membrane Science 375 (2011) 313–322

315

Fig. 1. Schematic drawing of a silicalite-1 composite membrane.

Pressures P1 and P2 , indicated in Fig. 1, are the pressures at the interfaces between the layers. The fluxes through layers S1 and S2 were accordingly expressed as [13]:

 JS1 =

194K0,S1

 JS2 =



B0,S1 (P1 + P2 ) T + M 2

B0,S2 (P2 + Ppermeate ) 2



 1 PS1 RT ıS1

mechanism in the defects, the following equation could be used to describe the flux through the defects, JiK

=

(1)

 A id



ATotal

id



97rid

r 2 (PF + P1 ) T + id Mi 16

 1 PFilm RT ı

(3)

3.3. Transport through zeolite pores in the film 1 PS2 RT ıS2

(2)

The supports used in the present work were identical to those used in our previous work [13,20] and thus similar parameter values for B0 and K0 were used in the model. The parameters K0 and B0 in Eqs. (1) and (2) were determined by single component permeation measurements of nitrogen, helium and argon through the support material before application of the zeolite film. By applying a non-linear optimization method, K0 and B0 values were fitted by minimizing the residual between the permeation fluxes calculated from Eqs. (1) and (2) and the experimental permeation data. As observed before [20], the calculations showed that the total pressure drop occurred predominately over the first layer S1 with the smaller pore size. The pressure drop over the second layer S2 was negligible, and thus its resistance was insignificant. Thus, the transport parameter (B0,S2 ) for layer S2 was not determined. The transport parameters K0,S1 and B0,S1 were found to be (6.02 ± 0.19) × 10−10 m and (9.85 ± 0.25) × 10−17 m2 , respectively.

Unlike the previous work [13] for single component diffusion where a Fickian model was assumed for transport through the zeolite pores in the film, the diffusion mechanisms were assumed to be the so-called surface diffusion and gas translational or activated Knudsen diffusion in the present work. The generalized Maxwell-Stefan diffusion formulation was applied for describing the multi-component surface diffusion, where the following equations were adapted from Krishna [16]. The surface diffusion flux JS was expressed in the (n × n)-dimensional matrix form, (J S ) = − j =

AZ [qsat ][B]−1 [ ]∇ () ATotal

qj

(5)

qsat,j

where the elements of the matrix [B] were

 j 1 + ; Dis Dijs n

Bii =

j=1

3.2. Transport through defects in zeolite film The method used to quantify the total defect area and size distribution from the permporometry measurement data was adapted from Hedlund et al. [17]. The area of a certain defect size is denoted Aid and if the total membrane area is ATotal then the area  of the nondefective film AZ could be estimated as AZ = ATotal − Aid . Details about the method to calculate the defect distribution is given in [17] and is summarized here. The defect size distributions were determined from the permporometry data by application of the Horvath Kawazoe (micropores) and Kelvin (mesopores) equations. Assuming that Knudsen diffusion was the dominating transport

(4)

Bij = −

i Dijs

(6)

Based on the Vignes empirical approach, for estimating the molecule interaction diffusivities Dij , the following logarithmic interpolation is used, Dijs = [Dis ]

i /(i +j )

[Djs ]

j /(i +j )

(7)

The single component adsorption equilibrium was expressed by the Langmuir adsorption isotherm, qi = qsat,i

Ki Pi ; 1 + Ki Pi

(8)

316

S.K. Wirawan et al. / Journal of Membrane Science 375 (2011) 313–322 Table 1 Adsorption and diffusion parameters (6 parameters unknown and fitted). Parameters Adsorption qsat [mol/kg] −H0 [kJ/mol] −S0 [J/mol/K] Surface diffusion S [× 10−8 m2 /s] Dm −E0S [kJ/mol] Gas translational diffusion GT [× 10−8 m2 /s] Dm −E0GT [kJ/mol]

Fig. 2. Transport pathways through the membrane by the different mechanisms. The mass transfer through the zeolite film was modeled by surface diffusion (1), activated Knudsen diffusion (2) and Knudsen diffusion (3) through the defects. The mass transfer in layer S2 was modeled by viscous flow (6), Knudsen (4) and viscous flow (5) in layer S1.

and the adsorption equilibrium constant (Ki ) could be expressed in terms of the enthalpy (H) and entropy (S) of adsorption as follows: Ki = e(−Hi /RT ) e(Si /R)

(9)

The multi-component adsorption isotherm was predicted using the ideal adsorption solution (IAS) theory [21], =

RT A



p=P 0 i

q0i (p)d ln p

(10)

p=0

Pyi = Pi0 q0i xi qtot =



(11)

qi =



1

CO2

5.4 [9] 5.9 [9] 43 [9]

2.025 [22] 23.6 [22] 74.9 [22]

unkown (fitted) unkown (fitted)

unkown (fitted) unkown (fitted)

4 [15] unkown (fitted)

4 [15] unkown (fitted)

the total pressures (P1 and P2 ) at each layer interface or connection node. Since the transport resistance in the support layer S2 was found to be negligible compared to that of layer S1, the total pressure between the two support layers (P2 ) is equal to Ppermeate . From the experiments, only the total pressures of the retentate and permeate (PFeed and Ppermeate ) were observed. The pressure between the inner layers (P1 ) was calculated iteratively by balancing the total molar fluxes through each layer via an optimization routine. In addition some parameters connected to certain transport mechanisms were unknown. To estimate these parameters, a second iteration loop was used. The total flux through the membrane (from single and binary gas permeation experiments) was fitted to the experimental data using LSQNONLIN, a non-linear regression function in MATLAB 6.5. The known and unknown parameters are listed in Table 1. To decrease the correlation among the fitted parameters some modification of the diffusivity expressions in Eqs. (15) and (16) were made. The surface diffusivity expression was reformulated as,

S DiS = Dm,i exp −

S E0,i

1

R

T

−

1 Tm

 (17)

(12)

xi /q0i

and the gas translational diffusivity as,

The contribution of flux from the gas translational diffusion mechanism was expressed as JiGT = −

H2

DiGT

PFilm,i AZ ATotal RT ı

(13)

 DiGT

=

GT Dm,i



GT E0,i T exp − Mi R

1 T

−

1 Tm

 (18)

where Tm is the mean experimental temperature, 148 ◦ C.

The total flux through the membrane was then, JiTOT

= JiS + JiGT + JiK

(14)

The temperature dependence of the surface and activated Knudsen diffusivities were expressed as,



DiS = Doi exp −

 DiGT = Doi

S EAi



(15)

RT



E GT T exp − Ai Mi RT

 (16)

3.4. Combination of mechanisms and parameter fitting Fig. 2 illustrates the mass transport pathways through the membrane by the different mechanisms. The pathways are connected at the interferences between layers by the pressures Pi . The method of line was used to model the transport in the zeolite film. The film was discretized into 50 elements to resolve the surface coverage gradients along the membrane thickness. However, discretization of the support layers was not necessary. To calculate the flux contributions from the different mechanisms, it was necessary to know

4. Results and discussion 4.1. SEM and adsorption branch n-hexane/helium permporometry A SEM image of the cross section of the same membrane used in the permeation experiments is shown in Fig. 3. The image indicates that there is some variation in the local film thickness, with an average film thickness of about 540 nm. Fig. 4 shows the adsorption branch n-hexane/helium permporometry pattern of the same silicalite-1 membrane used in the permeation experiments. A high quality membrane is indicated by a large drop in permeance between the points (p/p0 = 0 and p/p0 = 0.025) in the pattern [17]. For this membrane, the helium permeance decreased by 99.5% between these points, which shows that it is a high quality membrane. Using the method described in Section 3.2, the calculated total area of defects was found to be about 0.0047% of the total mass transport area. The estimated defect size distribution and areas are presented in Table 2. This small total defect area indicated that the silicalite-1 film of the composite membrane was of high quality.

S.K. Wirawan et al. / Journal of Membrane Science 375 (2011) 313–322

317

Table 2 Estimated defect distribution from permporometry data. He permeance (mol/m2 Pa s)

Relative pressure (P/P0 )

−6

9.117 × 10 6.904 × 10−8 4.835 × 10−8 4.234 × 10−8 3.869 × 10−8 3.582 × 10−8 3.152 × 10−8 3.055 × 10−8

0.0000 0.0090 0.0232 0.1369 0.2259 0.4520 0.7671 0.9903

Defect interval (nm)

– 1.65 1.90 2.91 3.69 6.43 17.75 –

– 1.65 1.65–1.90 1.90–2.91 2.91–3.69 3.69–6.43 6.43–17.75 >17.75

Defects relative area (%)a – – 3.45 × 10−3 7.14 × 10−4 3.23 × 10−4 1.69 × 10−4 1.06 × 10−4 1.61 × 10−5

Defect area divided by membrane area.

100

2

He Permeance, x 10 mol/(m .s.Pa)

a

Width of defects (nm)

-7

10

1

0.1 0

0.2

0.4

0.6

Fig. 3. SEM side view image of the silicalite-1 membrane used for the permeation experiments with average film thickness indicated.

1

Fig. 4. He permeance as a function of relative pressure of n-hexane in the permporometry measurement.

4.2. Single gas H2 and CO2 permeation Single gas permeation measurements at steady state were conducted for H2 and CO2 with the membrane pressure difference (P) from 0.3 to 0.8 bar and over the temperature range of 25–300 ◦ C. Fig. 5 shows the experimental H2 and CO2 fluxes, (illustrated by points) as a function of temperature. For both gases, the fluxes continuously decreased with temperature. Other authors have reported similar behaviors for these gases through silicalite-1 membranes when the pressure drop method was applied [14,23,24]. Fig. 5 also shows the model predictions (illustrated by lines) of the single component permeation fluxes and illustrates the excellent agreement between model and experimental data. At a given pressure gradient and temperature, H2 has a higher flux than CO2 under all conditions, which means the CO2 /H2 flux ratio is less than unity.

The single gas flux ratio of CO2 /H2 was calculated and is compared with the Knudsen flux ratio in Fig. 6. Under all conditions, the flux ratio is higher than the Knudsen limit, indicating that there are other mechanisms involved in the overall mass transport, i.e. surface diffusion and/or activated Knudsen diffusion. Since the permporometry results indicated a very small defect fraction, the Knudsen contribution via defects to the overall transport should be very low, but the Knudsen effect through the support resistance may have some importance. The fact that the CO2 /H2 flux ratio decreases with temperature and approaches the Knudsen ratio is an indication that surface diffusion probably gives a significant contribution to the overall transport. It is known that CO2 is more strongly adsorbed that H2 , and the enthalpy of adsorption of CO2 is greater than that of H2 in silicalite-1 (see Table 1). As a result, the sur-

2250

1250 dP = 0.4 bar (exp)

2000

dP = 0.4 bar (exp)

dP = 0.5 bar (exp)

1750

dP = 0.6 bar (exp)

1500

dP = 0.7 bar (exp) dP = 0.8 bar (exp)

1250

dP = 0.5 bar (exp)

1000

Fluxes (mmol/m 2.s)

Fluxes (mmol/m 2.s)

0.8

Relative Pressure (P/P0)

1000 750 500

dP = 0.6 bar (exp) dP = 0.7 bar (exp)

750

dP = 0.8 bar (exp)

500

250

250 0

0 0

50

100

150

200 o

Temperature ( C)

250

300

0

50

100

150

200

250

300

o

Temperature ( C)

Fig. 5. Single permeation fluxes versus temperature for H2 (left) and for CO2 (right). The symbols are experimental data and continuous lines are the simulation results.

318

S.K. Wirawan et al. / Journal of Membrane Science 375 (2011) 313–322

CO2/H2 Single Permeation Flux Ratio

0.8

Knudsen ratio dP = 0.4 bar dP = 0.6 bar dP = 0.8 bar model dP=0.8 bar model dP=0.6 bar model dP=0.4 bar

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

50

100

150

200

250

300

o

Temperature ( C) Fig. 6. CO2 /H2 single permeation flux ratio compared to Knudsen ratio. The symbols are experimental data and continuous lines are the simulation results.

face concentration of CO2 will decrease more than that of H2 with increasing temperature which in turn leads to a relatively larger decrease in the flux of CO2 . It is difficult to reveal the transport mechanisms of H2 and CO2 through a zeolite membrane directly from experimental results and determine whether a single transport mechanism represents the true transport. Transport mechanisms suggested in the literature can be ambiguous. For example, in [24] and [25] for a temperature range of 4–450 ◦ C, H2 transport through an MFI zeolite membrane is modeled via pure surface diffusion, in [5] activated gas diffusion is assumed over a temperature range of 27–464 ◦ C, whereas in [14] and [23], Knudsen diffusion is considered to prevail at similar temperature conditions as the present work. At higher temperature, it is unlikely that a large amount of H2 undergoes surface diffusion, since the adsorption of H2 is quite weak compared to that of CO2 . It has been suggested that as a rule of thumb, activated diffusion starts to come into play at a ratio of the kinetic diameter versus the pore diameter in the range of 0.6–0.8 [15]. Considering the ratio of the H2 kinetic diameter to the pore diameter (0.29 nm/0.55 nm ≈ 0.53), it may be suggested that its diffusion process is almost not activated. Since the defects are larger than the zeolite pores (see Table 2), there should not be a need for an activation for gaseous molecules like H2 and CO2 to pass. The defects are also not large enough to allow for a significant contribution of viscous flow. The range of mean free paths of H2 and CO2 under the experimental conditions also only approaches the largest and least abundant defect pore size (100 nm). Therefore, the resulting mechanism for the transport of H2 and CO2 through the defects is assumed to be Knudsen diffusion. It can be difficult to distinguish between the amount of gases permeating through the defects from that transported through the zeolite pores as an activated process based only on steady-state permeation data. This is especially the case if the activation energy for diffusion in the zeolite is small as it may be for H2 .

Fig. 7. CO2 and H2 fluxes as a function of temperature for a feed comprised of 50/50 H2 /CO2 . Solid lines illustrate the results from the fitted model including support resistance, broken lines illustrate the results from the fitted model without the support and symbols are experimental results.

The H2 maximum flux occurs at a slightly higher temperature than that for CO2 . For the fluxes observed for the equimolar feed composition illustrated in Fig. 7, the H2 flux reaches a maximum of 250 mmol/(m2 s) at about 90 ◦ C and for CO2 the maximum is 265 mmol/(m2 s) at about 75 ◦ C. When the feed composition is 70/30 H2 /CO2 , the maximum H2 flux reaches 365 mmol/(m2 s) at 80 ◦ C and for CO2 the maximum flux is 169 mmol/(m2 s) and occurs at a temperature almost equal to that for the equimolar feed. These observations can be explained using the adsorption and diffusion theory. At low temperatures, the amount of gas adsorbed in the zeolite pores is high, and the flux increases with temperature because the mobility of the adsorbed molecules increases, although the surface coverage decreases. However eventually, the flux begins to decrease when the increase in mobility cannot compensate for the decrease in surface coverage. In this temperature range, the transport probably occurs mainly via adsorption followed by surface diffusion. Fig. 7 also shows that at temperatures below 105 ◦ C, the flux of CO2 is higher than that of H2 and above that temperature, the trend switches to where the H2 flux is higher. This trend is also repro-

4.3. Binary H2 /CO2 gas permeation Figs. 7 and 8 show the experimental binary permeation fluxes (points) for two different feed compositions as a function of temperature for a feed pressure of 1.4 bar and a permeate pressure of 1 bar. Fig. 7 illustrates the results for an equimolar H2 /CO2 (50/50 H2 /CO2 ) feed mixture, while Fig. 8 illustrates the results for a feed with a molar ratio of H2 to CO2 of 70/30. For both flux profiles, starting at low temperature, the H2 and CO2 fluxes increase to maximum values and then continuously decrease.

Fig. 8. CO2 and H2 fluxes as a function of temperature for a feed comprised of 70/30 H2 /CO2 . Solid lines illustrate the results from the fitted model including support resistance, broken lines illustrate the results from the fitted model without the support and symbols are experimental results.

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duced by the simulations. It is well known that surface diffusion is a function of surface coverage, in this case CO2 is adsorbed stronger than H2 and CO2 dominates the surface coverage if the gas concentration of CO2 is sufficient, such as the case with the equimolar feed composition. At low temperature, the CO2 blocks the surface and hinders the passage of the faster moving H2 molecules. At higher temperature, the surface coverage of CO2 drops greater than that of H2 molecules and CO2 becomes increasingly less effective at blocking the passage of H2 . On the other hand, when the feed composition is 70/30 H2 /CO2 , the flux of H2 is higher and the flux of CO2 is lower, since the driving forces are different. At these conditions, the flux of H2 is always superior to that of CO2 over the temperature range observed, as depicted in Fig. 8. Generally, as shown in Figs. 5–8, simulations from the same model reproduced both the observed single and binary fluxes. It should be pointed out that the observed single gas permeances are quite close to the observed mixture permeances in the present work, where the pressure drop method was used in the permeation experiments. For instance, the mixture CO2 permeance at room temperature (50/50 mixture) is about 105 × 10−7 mol/(m2 s Pa) and the single gas CO2 permeance is only about 25% higher. We have previously reported that quite different mixture permeances (6 times lower) compared to single gas permeances are observed when sweep gas is used in the mixture experiments but not in the single gas experiments [28]. However, there are some deviations between the simulations and experimental data. It is evident that the model slightly underestimates the CO2 flux when the feed concentration is 70/30 H2 /CO2 (see Fig. 8). In our model, the multi-component adsorption is predicted by IAS theory, based on single gas adsorption on silicalite-1 powder. The IAS theory does not account for possible interactions between adsorbed species at high coverages which in turn influences diffusion in the silicalite-1 membrane. Based on the calculations, the surface diffusion contribution dominated the overall mass transport. According to the model, more than 99% of the overall CO2 transport through the zeolite film was accounted for by surface diffusion, whereas for H2 , surface diffusion accounted for about 98.5% of the overall mass transport at room temperature. The exact fractional contributions to the total fluxes varied with temperature although the overall CO2 transport through the zeolite film was always more than 98.5% accounted for by surface diffusion. As depicted in Fig. 9, at higher temperature, the transport through the film by gas translational diffusion steeply increases at the expense of the surface diffusion although surface diffusion is still dominant. At a temperature of about 300 ◦ C, the gas translational diffusion flux fraction for H2 is about 1.2% and that for CO2 it is less than 0.2%. For Knudsen diffusion (only in the defects in the film), the fractional contributions were found to slightly increase for CO2 and decrease for H2 . A somewhat different behavior for the 50/50 H2 /CO2 binary mixture permeation has been reported in the literature. Kapteijn et al. [6] presented experimental data showing the flux profiles for a 50/50 H2 /CO2 binary mixture permeating through a 40 ␮m thick silicalite-1 membrane as a function of temperature. In their results, the CO2 flux reached a maximum and then decreased at higher temperatures. However in contrast to our results, H2 exhibited a nearly steadily increasing flux as a function of temperature. They measured the gas fluxes with He sweep gas and no pressure drop across the membrane, whereas our measurements were made with pressure drop and no sweep gas. However, these experimental differences (pressure drop/sweep gas) may only be partially responsible for the different behavior observed. It should also be noted that the zeolite film thicknesses also differ vastly and the methods used to synthesize the zeolite films were different which likely means they have different morphologies. In addition, in Kapteijn et al. [6] no attempt was reportedly made to quantify the quality of the membrane nor the fraction of the total diffusion

319

Table 3 Diffusion parameters obtained from model (6 parameters) and compared to reported literature values. Parameters Surface diffusion S [× 10−8 m2 /s] Dm −E0S [kJ/mol] Gas translational diffusion GT [× 10−8 m2 /s] Dm −E0GT [kJ/mol] a

H2

CO2

2.68 ± 1.09 1.8 [24] 3.89 ± 1.37 2.0 [24]

15.4 ± 3.7 0.70 [26] 13.4 ± 0.82 9.6 [26]

4 [15]a 43.6 ± 11.7

4 [15]a 51.9 ± 19.9 10.3 [26]

The bold values are fixed.

through defects in the zeolite film. As a result, it is likely that differences in the transport mechanisms through the zeolite films also contributed to the observed differences in the flux-temperature profiles. The formation of intercrystalline pore openings at elevated temperatures, caused by strain due to differences in thermal expansion of zeolite film and support [24,27], may also contribute to differences in experimental results. These intercrystalline pores would contribute to increasing flux when temperature increases and may explain why others have observed what appeared to be significant amounts of gas translational diffusion of CO2 and H2 [5,6] within a temperature range where our results indicate that surface diffusion is dominant. The formation of intercrystalline pore openings with temperature is considered to be more prevalent on thick multilayer crystal films and less likely on films, as ours, chiefly consisting of a single layer of intergrown zeolite crystals [27]. 4.4. Model analysis A complete composite membrane model was used to simulate and fit the experimental data for both single and binary gas permeation. Both the single and binary permeation model and experiments were optimized together to obtain the values of the fitted parameters by minimizing the sum of square errors (SSE). The values of the fixed and 6 fitted parameters compared with literature values are presented in Table 3. The fixed values of the adsorption parameters are shown in Table 1 above. As an alternative approach of fitting, all of the adsorption parameters were also fitted. This approach yielded fitted adsorption parameters, which were close to the literature values with small confidence intervals and a slightly better fit to the experimental permeation measurements. Apparently, the experimental data was sufficient even to resolve the adsorption parameter values, and the general suitability of the reported literature values could be confirmed. In Table 3, the 6 fitted parameter values are presented along with their 95% confidence intervals. The low confidence intervals of the values obtained by regression indicate that correlation between the fitted parameters was low and the parameter values could be resolved from the experimental data. In addition, the model could adequately represent the experimental data with reasonable values of fitted parameters compared to reported literature values. The fitted activation energies of H2 and CO2 for activated Knudsen diffusion of about 43.6 and 51.9 kJ/mol respectively are in the range of commonly reported values in the literature (5–60 kJ/mol) GT of [15]. However, the fixed pre-exponential factor values, Dm 4 m2 s−1 are theoretical estimates given by Xiao and Wei [15] based on the coordination number and diffusion length in the MFI zeolite structure. Our preliminary optimization showed that when preGT were fitted, large confidence intervals were exponential factors Dm obtained which indicated that these parameters had only a small influence on the model predictions.

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1.5

1.5

b

Hydrogen - GT Hydrogen - KD Carbondioxide - GT Carbondioxide - KD

Fluxes Fraction (%)

Fluxes Fraction (%)

a

1

0.5

Hydrogen - GT Hydrogen - KD Carbondioxide - GT Carbondioxide - KD

1

0.5

0

0 0

50

100

150

200

250

0

300

50

o

100

150

200

250

300

o

Temperature ( C)

Temperature ( C)

Fig. 9. Model predictions of percentage of flux contributions to the total permeation fluxes through the film as function of temperature; KD: permeation fluxes via Knudsen diffusion (in defects); GT: permeation fluxes via gas translational diffusion (in zeolite pores); (left) feed composition of 50/50 H2 /CO2 ; (right) feed composition of 70/30 H2 /CO2 .

In addition, changing the fixed pre-exponential value was not found to affect the fitted parameters results since the contribution of the gas translational diffusion to the overall transport was small. The gas translational activation energies may have been of greater importance since the gas translational contribution to the total transport increased rapidly at higher temperature. Nevertheless, gas translational diffusion is arguably negligible over the experimental conditions; however it was not excluded from the model because it should be included in a complete transport model and an evaluation of all possible transport mechanisms. Parameter fitting also resulted in activation energy for surface diffusion E0S for H2 and CO2 of 3.89 and 13.4 kJ/mol respectively. The activation energies for the surface diffusion found in the present work seem to also be in reasonable agreement with values reported in the literature [24,26], in particular in the case of CO2 . There is a larger difference for H2 probably because its weaker surface diffusion is prone to less accurate estimation. The heat of adsorption, H, for CO2 in this present work is 23.6 kJ/mol, which is much greater than its activation energy for surface diffusion. It is reasonable that it should require more energy for a CO2 molecule to completely desorb into the gas phase rather than transfer from one adsorption site to another. Similar results were also found for H2 . To determine the effect of the support, the fitted parameters have been used to simulate the fluxes through the composite membrane in the absence of the support resistance (‘no support model’), but with the same total pressure drop (i.e. driving force) over the membrane. These simulated fluxes were compared with those calculated by the original model which included the support resistance (‘support model’). The simulated fluxes in the absence of support resistance are presented in Figs. 7 and 8 with dashed lines. As shown in Figs. 7 and 8, the average permeation fluxes of the ‘no support model’ were found to be 80% higher for H2 and 76% higher for CO2 compared to the ‘support model’. It was also found that the pressure drop over the support was about 43% of the total pressure drop across the composite membrane, in line with our previous reports [13]. These results show that the transport resistance of the support is not at all negligible. By comparing the CO2 /H2 separation factor (flux ratio divided by feed composition ratio) it was found that at temperatures lower than 100 ◦ C, the separation factor calculated by the ‘no support model’ was up to 14% higher compared to that calculated by the ‘support model’. As expected, the support resistance also influences the overall membrane selectivity especially at lower temperatures. This is because at low temperature, the surface diffusion mechanism in the zeolite film favors CO2 per-

meation, however this is countered by H2 permeation being favored by Knudsen diffusion in the support. 4.5. Model prediction In order to estimate the membrane performance at elevated pressure and lower temperatures, beyond the experimental range used here, the developed model with fitted parameters was used to predict the separation factor at various pressure ratios and temperatures. The pressure ratio PR is defined as: PR =

Pfeed Ppermeate

(19)

The separation factor is defined as the flux ratio divided by the mole fraction ratio in the feed, JCO2 /JH2 CO2 separation factor = , H2 xCO2 /xH2

(20)

In the model predictions, the permeate pressure was set at 1 bar, and the pressure ratio was varied from 1.4 to 10 for a feed gas composition of 50/50 H2 /CO2 . The simulation result is illustrated in Figs. 10 and 11.

Fig. 10. Estimated CO2 /H2 separation factor as a function of temperature and pressure ratio (PR) for a feed comprised of 50/50 H2 /CO2 and atmospheric permeate pressure.

S.K. Wirawan et al. / Journal of Membrane Science 375 (2011) 313–322

and a feed pressure of 10 bar and atmospheric permeate pressure.

6000 5000

9

4000

α

7

3000 5 2000

Feed : CO2/H2 = 50:50

J

o

T=0 C P permeate = 1 bar

3

1000

1

CO2 Fluxes, J (mmol/m2.s)

CO2/H2 Separation Factor, α

11

0 1

2

3

4

5

6

7

8

9

321

10

Pressure Ratio, PR (bar) Fig. 11. Estimated CO2 /H2 separation factors and CO2 fluxes as a function of pressure ratio (PR) for a feed comprised of 50/50 H2 /CO2 at 0 ◦ C.

At room temperature and a pressure ratio of 1.4 (the experimental condition of this work), the CO2 /H2 separation was about 1.3. The separation factor increased significantly up to 5.5 at a pressure ratio of 10. These model predictions of achievable separation factors should however be regarded with caution since Langmuir adsorption isotherms may be less reliable at high surface coverage. However as illustrated in Fig. 11, at 0 ◦ C and a pressure ratio of 10 the predicted separation factor reaches about 9.8 with the estimated CO2 flux as high as 4290 mmol/(m2 s) which almost 17 times higher than the maximum flux observed experimentally at a pressure ratio of 1.4. In summary, these predictions indicate excellent membrane performance at high pressure ratios and low temperature (0 ◦ C). 5. Conclusion Single and binary H2 /CO2 gas permeation through a silicalite1 composite membrane was studied both by experiments and modeling. A complete model that combines the different transport mechanisms for the simulation of mass transfer through the silicalite-1 composite membrane was presented. The single component permeation results showed a decreasing flux with increasing temperature. The fact that the CO2 /H2 flux ratio did not correspond to the Knudsen ratio revealed that there was a combination of transport mechanisms including; Knudsen diffusion in the support, surface and gas translational diffusion in the zeolite film as well as Knudsen diffusion through defects in the film. Permporometry results revealed that the thin silicalite-1 film (540 nm) of the membrane was of high quality, i.e. the estimated defect area was only 0.0047% of the total membrane area. The approach used here of quantifying the transport contribution through defects based on permporometry measurements better distinguishes the contribution given by Knudsen diffusion through defects from gas translational diffusion in the film. For a membrane with an ultra thin zeolite layer as used in this study, the effect of the support on the permeation fluxes was clearly not negligible. The transport resistance through the support was significant and it could influence the permeation selectivity of the membrane under conditions where the permeation selectivity due to Knudsen diffusion in the support opposed the selectivity due to surface diffusion in the film. However, in general the model could adequately represent the experimental data with reasonable diffusion parameters. Surface diffusion is the dominating mechanism for H2 and CO2 transport through the zeolite film in a silicalite1 composite membrane in the temperature range of 25–300 ◦ C. It was found to account for at least 98% of the transport. The model predictions indicated that a CO2 /H2 separation factor exceeding 9 and a CO2 flux exceeding 4 mol/(m2 s) could be obtained at 0 ◦ C

Acknowledgements The authors are grateful for the financial support of the Swedish Energy Agency and the SIDA-Swedish Research Links program for supporting collaborative research activities between Chemical Reaction Engineering, Chalmers University of Technology, Sweden and the Department of Chemical Engineering, Gadjah Mada University, Indonesia. Jonas Hedlund acknowledges the Swedish Foundation for Strategic Research and Bio4energy for financial support. The Knut and Alice Wallenberg foundation is acknowledged for financially supporting the Magellan SEM instrument.

Nomenclature Roman symbols A mass transfer area, m2 [B] square matrix of inverse Maxwell-Stefan coefficients, m−2 s B0 viscous flow constant, m2 D diffusivity, m2 s−1 EA activation energy, J mol−1 K0 Knudsen constant, m M molecular weight, kg mol−1 J permeation flux, mmol m−2 s−1 P total pressure, bar equilibrium pressure for pure i corresponding to Pi0 () spreading pressure  q molar loading, mol kg−1 qsat saturation loading, mol kg−1 qtot total loading, mol kg−1 r defects radius, m R universal gas constant, bar m3 mol−1 K−1 T temperature, ◦ C x mol fraction in adsorbed phase y mol fraction in gas phase Greek symbols  viscosity, N s m−2 ı composite membrane layer thickness, m  density, kg m−3  fractional occupancy [] matrix of thermodynamic factor  spreading pressure Subscript F feed i component i j component j m at mean temperature 0 standard state S1 first alumina layer S2 second alumina layer tot total id defects Z non-defective zeolite film Superscript K Knudsen diffusion S surface diffusion GT gas translational diffusion

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