Ideal separation factor

The flux, and hence the permeance and permeability, can be defined on the basis of volume, mass or molar flowrates. The accurate prediction of permeabilities is generally not possible and experimental values must be used. Permeability generally increases with increasing temperature. Taking a ratio of two permeabilities defines an ideal separation factor or selectivity awhich is defined as ... 

Liu et al. [42] reported permeation of mixture of hexanes and octanes through silicalite membranes. It was found that the permeances of the mixture could not be predicted by the single-component data. In the separation of alkane isomers, the permeance of 2,2-DMB is significantly reduced in the presence of n-hexane resulting in a permselectivity much higher than the ideal separation factor [7]. 

The values of permeability coefficients for He, O2, N2, CO2, and CH4 in a variety of dense (isotropic) polymer membranes and the overall selectivities (ideal separation factors) of these membranes to the gas pairs He/N2,02/N2, and CO2/CH4 at 35°C have been tabulated in numerous reviews (Koros and Heliums, 1989 Koros, Fleming, and Jordan et al., 1988 Koros, Coleman, and Walker, 1992). Moreover, several useful predictive methods exist to allow estimation of gas permeation through polymers, based on their structural repeat units. The values of the permeability coefficients for a given gas in different polymers can vary by several orders of magnitude, depending on the nature of the gas. Thevalues oftheoverall selectivities vary by much less. Particularly noteworthy is the fact that the selectivity decreases with increasing permeability. This is the well-known inverse selectivity/permeability relationship of polymer membranes, which complicates the development of effective membranes for gas separations. 

Knudsen diffusion P = Permeability (barrer or 10 indicates ideal separation factor, (S.F.)kd - 0.94... 

Alumina membranes made by anodic oxidation were tested for separating hydrogen and carbon monoxide at a temperature up to 9T C [Itaya, 19S4], The ideal separation factor only achieved 3.5. See Table 7.4. Wu et al. [1993] also examined the use of alumina membranes for this application at an even higher temperature of 300 C and obtain a maximum separation factor of only 2.2. The alumina membranes used in the above studies all have pore diameters larger than 4 nm. Their separation factors for the H2/CO gas pair are no higher than the Knudsen diffusion values of 3.7 most likely as a result of the limitation imposed by the relatively large pores involved. 

On the other hand, actual binary mixture tests using porous alumina and glass membranes show separation factor values for helium recovery from oxygen that are lower than what Knudsen diffusion provides, as indicated in Table 7.15. Only Koresh and Soffer [1983a 1983b] show an ideal separation factor of 20 to 40 with a low permeability of 1.2x10 barrers when molecular sieve membranes with a reported pore diameter of 0.3 to 0.5 nm are used. 

Figure 7.6 Ideal separation factor of helium/nitrogen with a scries of silica-modified membranes at 25 C [Lin ei al., 1994J...

Figure 9.1 Trade-off curve between the ideal separation factor of CO2/CH4 and the CO2 permeability [Koros and Fleming, 1993]...

P/l is also referred to as permeability flux and expressed as (m (STP)/(m bar h)). Ap, is the partial pressure difference of i across the membrane measured in pascals or bars. This equation shows that the flux through the membrane is proportional to the pressure difference across the membrane and inversely proportional to the membrane thickness. Por selectivity between gas components the Equations 4.3 and 4.4 are referred to. The ideal separation factor, a (Equation 4.3), may be expressed by the ratio of the pure gas permeabilities for the individual components i and j. 

Table 1. Permeability of polymers and ideal separation factors for composite hollow fiber membranes (20 °C).

In mesoporous membranes the most effective separation mechanism outside the capillary condensation region is Knudsen diffusion. In this case the ideal separation factor a equals the square root of the ratio of masses ... 

In general a is not equal to a due to back diffusion, caused by non-zero pressure at the permeate side, or to contributions of non-separative mechanisms to the total flow and concentration polarisation on feed or the permeate side. Also the presence of surface diffusion influences the ideal separation factor. 

As discussed above, the ideal separation factor a in the case of pure Knudsen diffusion is given by Eq. (9.37) and is equal to the permselectivity provided that surface diffusion is not present (high temperature). As can be seen from (9.37) the highest ideal separation factors are obtained for mixtures of light and heavy gases. Back-diffusion effects are taken into account by Eq. (9.38) to give the real separation factor. 

The effect of the pressure, temperature and pore radius on the separation factor is investigated also by Eichinann and Werner [19] using Eq. (9.34) with a constant and experimentally determined value of P for eiU gas membrane combinations, in contrast to Wu et al. who fitted the value of p for each gas membrane combination. Figure 9.14 shows the effect of the pressme ratio Pj. for different mean pressure levels P (assuming a linear pressure drop in the membrane) on the separation factor of a N2/CO2 mixture (ideal separation factor equals 1.25) in a membrane with pore radius Rp = 0.03 pm. 

Separation factor. Subscript 0 ideal separation factor (Eqs. (9.36) or (9.38))... 

Figure 3. Correlation between the solubility parameter of several glassy polymers and the Ideal separation factors for the CO2/CH. system calculated using the pure component permeabilities at 35 for a 20 atm upstream pressure of each component.

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