Pressure dependency of permeability

Figure 10. Pressure-dependence of permeability rate of asymmetric...

The ideal separation foctor, equal to the ratio of the permeabilities of the two components, is also inteipretable as a product of two factors a "solubUiQr selectivity and a "mobiUty selectivity. These two selectivity contributions, consisting of the ratios of the respective conqionent solubilities and diffiisivities, indicate the relative importance of thermodynamic and kinetic fecKirs in the permselection process. Unfortunately, optimization of product permeability and membrane selectivity is oftmi difficult, and trade-offs in the two parameters may be necessary on economic grounds. A brief discussion of characterization methods and typical forms of sorption isotherms and local difiiiaon coeffidents for gases and vapors in polymers is presented below. This discussion serves as a background for rationalizing pressure dependencies of permeabilities and selectivities. 

This plasticization phenomena can be observed in some glassy polymers exposed to high pressures of condensable gases, such as CO2. Moreover, a pressure dependence of permeability occurs for glassy polymers prior to plasticization, whereas rubbery materials tend to have essentially pressure-independent permeabilities. The decrease in permeability of component A with increasing partial pressure of either component A or B prior to the onset of plasticization (70) shown in Figure 21 (71) is characteristic of glassy polymers. 

Gavrilenko, P., Gueguen, Y., 1989. Pressure dependence of permeability a model for cracked rocks. Geophys. J. Int. 98, 159-172. 

Sigal, R.F., 2002. The pressure dependence of permeability. Petrophysics 43, 92—102. March-... 

The studies where the permeability coefficients were measured at gas pressures changing in a reasonably wide range revealed them to be pressure dependent, typically decreasing upon the pressure increase. The exceptions are helium and hydrogen where no pressure dependence has been reported. For some other permanent gases (e.g. nitrogen and oxygen) pressure dependencies of permeabilities are also rather weak. 

Comparing the curves in Fig. 2 shows that representing the permeability versus pressure data by either model provides a satisfactory fit to the data over the pressure range of 1 to 20 atm. However, at pressures less than 1 atm. the two models differ in their prediction regarding the behavior of the permeability-pressure curve [Fig. 2]. While the matrix model predicts a strong apparent pressure dependence of the permeability in this range (solid line), the dual-mode model predicts only a weak dependence (broken line). 

Figure 5.2 Experimental dependence of permeability upon mean pressure for helium and nitrogen through silica gel (adapted from Grachev [10]).

Figure 18 Pressure dependence of the CO2 permeability through a microporous glass membrane. Experimental results are compared to theory of combined gaseous and surface flow. (I Barrer = 3.35 X 10" mol m m Pa -sec". ) (Adapted from Ref. 38.)...

Pressure Dependence of Hydrocarbon Permeability in Rubbery Polymers Effect... 

FIGURE 9.25 Dependence of permeability coefficients of propylene PcsHe propane Pcshs and selectivity on partial pressure for the equimolar gas mixture in 6FDA-TrMPD polyimide (total pressure 3.1 10 Pa, T = 323 K). For comparison, the corresponding data for individual components designated with open symbols. (From Tanaka, K., Taguchi, A., Hao, J., Kita, H., and Okamoto, K., J. Membr. Sci., 121, 197, 1996. With permission.)... 

FIGURE 9.26 Time dependence of permeability coefficients for the mixture of gases CH4/C2H4/C2H6 (71%/19%/10% mol) for the membrane based on poly-2,6-dimethyl-l,4-phenylene oxide (pressure of the mixture 5x10 Pa, 7= 298 K). (From Lapkin, A.A., Roschupkina, O.P., and Dinitch, O.M., J. Membr. Sci., 141, 223, 1998.)... 

T)q)ical data for dense membranes are collected in Table 9.16. A full discussion of these data is outside the scope of this chapter. Using permeation values the reader should be aware of the fact that the pressure dependence of the flux is usually strongly non-linear, but takes the form of a power law with values for the exponent around 0.5. This makes direct comparison on the basis of permeance or permeability not meaningful. Furthermore, the permeation value is limited by surface reactions with a critical thickness varying between 0.1 and 2 mm depending on material and condition. 

Accurate description of barrier films and complex barrier structures, of course, requires information about the composition and partial pressure dependence of penetrant permeabilities in each of the constituent materials in the barrier structure. As illustrated in Fig. 2 (a-d), depending upon the penetrant and polymer considered, the permeability may be a function of the partial pressure of the penetrant in contact with the barrier layer (15). For gases at low and intermediate pressures, behaviors shown in Fig. 2a-c are most common. The constant permeability in Fig.2a is seen for many fixed gases in rubbery polymers, while the response in Fig. 2b is typical of a simple plasticizing response for a more soluble penetrant in a rubbery polymer. Polyethylene and polypropylene containers are expected to show upwardly inflecting permeability responses like that in Fig. 2b as the penetrant activity in a vapor or liquid phase increases for strongly interacting flavor or aroma components such as d-limonene which are present in fruit juices. 

Stern, Frisch, and coworkers have extended Fujita s free-volume model to the permeation of light gases (31-33) (see Figure 3) and binary gas mixtures (34,25) (see Figure 4) through polymer membranes. The extended model was found to describe satisfactorily the dependence of permeability coefficients on pressure and temperature for a variety of light gases in polyethylene, as well the dependence on composition for several binary mixtures in the same polymer. The validity of the extended model is limited to total penetrant concentrations of up to 20-25 mol-%. 

Figure 4. Permeation of a 50-mole% C02 - 50-mole% C2 H4 mixture through polyethylene. Dependence of permeability coefficients for C02 on applied partial pressure of C02. (S. A. Stern, G. R. Mauze, and H. L. Frisch,...

Accurate engineering modeling of membrane-based gas peimeaiors can be performed if the composition and pressure dependence of the various component permeabilities are known ai the temperature of interest. Permeabilities or gases and vapois have been reported to display behaviors represented by Figure... 

FIGURE 20.3-9 Pressure dependence of the permeability of various polymers to COj. The data wises measured with a vacuum downstream except for the cellulose acetate (CA). which was estimated from a variety of sources.21... 

Equation (14.42) suggests that the separation parameter Pc for a mixture could be evaluated from measurement of the slope factor S obtained from the pressure dependence of the permeability for a pure gas, Eq. (14.10). For real barrier materials it is found that the separation parameter p is appreciably smaller than would be predicted from the slope factor in Eq. (14.10). 

The linear pressure dependence of the gas permeability in function of the mean pressure suggests a viscous flow regime. Therefore, the permeability of the support can be improved by increasing gas pressure. In working conditions, the porous support is exposed to air pressure at 3 bars (0.3 MPa) that enables to reach a sufficient permeability of 2.9 x 10 mol.m . s Pa ... 

Determination of concentration-dependent diflusion coefficient data usually is done indirectly. Typically, one determines D(.C) from the observed pressure dependence of die permeability in conjunction with the independently (tetermined dC/dp data discussed in die ptecedii section. When significant concentration dependence is observed for the local difliision coefficients, the fi m generally resembles one of die corves shown in Fig. 20.3-fi. Of course, for low-sorbing gases such as Hj and N2 in rubbery polymer, both D and dC/dp are essentially constant resulting in adherence to die simple situation indicated Iqr Eq. (20.1-5). 

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