This sample run investigates the permeation of C1, C2, C3 and nC4 across a MFI membrane at 300 K. The upstream partial pressures of each component are held at 25 kPa. The downstream partial pressures are maintained at vanishing values by means of a sweep gas. The membrane has a thickness of 40 mm and the MFI zeolite has a density of 1800 kg/m3. Table 1 summarizes Langmuir parameters and Maxwell Stefan diffusivities for pure components.
|
Component |
Dual Langmuir Parameters |
|
|||
|
Site A |
Site B |
|
|||
|
bi,A /[Pa-1] |
Qi,sat,A /[molecules per unit cell] |
bi,B /[Pa-1] |
Qi,sat,B /[molecules per unit cell] |
Ði / [m2 s-1] |
|
|
C1 |
4.86 ´10-6 |
11.0 |
2.38 ´10-7 |
8.0 |
10-9 |
|
C2 |
9.73 ´10-5 |
12.0 |
4.38 ´10-7 |
3.0 |
1.5 ´10-10 |
|
C3 |
9.64 ´10-4 |
11.0 |
5.06 ´10-6 |
1.0 |
3.4 ´10-11 |
|
nC4 |
1.63 ´10-2 |
9.0 |
1.14 ´10-5 |
1.0 |
10-11 |
Table 1: Pure component data used for C1, C2, C3 and nC4
The animation in Fig. 1 shows the change of loadings along the membrane diffusion path with time, and the corresponding downstream permeation fluxes. In Fig 1 (a) the calculations include finite interchange Maxwell Stefan diffusivities, Ðij. The corresponding simulation results with infinite Ðij are shown in Fig. 1 (b). It is interesting to note that for finite Ðij the permeation of C1 is virtually suppressed in the presence of the more strongly adsorbing components C2, C3 and nC4. For infinite Ðij the permeation of C1, C2 and C3 exhibits high peaks during the initial transience. Also, the nC4/C3, C3/C2, C2/C1 permeation selectivities are significantly lower than for the case with finite Ðij.
Figure 1: Loading profiles along the membrane diffusion path and permeation fluxes across an MFI zeolite membrane at 300 K for an equimolar quaternary mixture of C1, C2, C3, and nC4. The isotherm data is specified in Table 1. The Maxwell Stefan diffusivities are taken from the thesis of Van de Graaf (1999). The simulations have been performed using two implementations of M-S model, (a) with and (b) without inclusion of the interchange coefficient Ðij.
The reason for the peaks is that during the initial period, C1, C2 and C3 diffuse faster through the membrane than nC4. However as time progresses and the MFI structure gets increasingly occupied with nC4 that dislodges the less-strongly adsorbing components. It is interesting to note that this effect also might cause a maximum in the loading profiles; see Fig 1. Furthermore, the flux of nC4 is enhanced with increased nC4 loading. Concomitantly, the fluxes of the less strongly adsorbing components decrease due to their decreasing loadings in the MFI. Besides, the Maxwell-Stefan interchange coefficient Ðij serves to slow down fast diffusing components and speed up slow diffusing components. All these factors leads to a decline in the flux of C1, C2 and C3 compared with the infinite Ðij case; compare Fig 1 (a) and (b).
Kapteijn et al. (2000) and Krishna and Paschek (2002) have analyzed permeation data for C1-C2 and C1-C3 mixtures across a MFI membrane to stress the need for recognizing the size entropy effects (with the use of the IAST model) and the importance of including finite interchange coefficients Ðij in the M-S formulation.
Further details and reading can be found in Krishna and Baur (2003).