Countercurrent gas permeation

In the ELM system there is no substrate as such we have simply the liquid membrane resistance beside the two film resistances, unless interfacial resistances exist. The presence of surfactants at the ELM interfaces is relevant 

To start with we adopt the formalism of equations (7.2.3) and (7.2.5) under the assumptions of no concentration polarization and no longitudinal diflusion/dispersion in the bulk flow direction (z-coordinate), and obtain for species A permeation through membrane area dA over a length dz  

For a rectangular feed-gas flow channel of width W and length L, 

we can express the left-hand side of equation (8.1.415) as 

For a hollow fiber device with a symmetrical hollow fiber membrane of diameters di and d and total number of fibers being n, 

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Table 17-4. Development of design equations for binaiy, countercurrent gas permeation...

Figure 8.1.51. (a) Schematic for a countercurrent gas permeator (b) permeate O2 composition vs. stage cut for a silicone copolymer membrane having Oqz-nz = 2.4, y = 0.2. The plots are qualitative and indicate the relative performance of a countercurrent permeator, vts-d-vis a crossflow permeator (Figure 7.2.1(a)) and a cocurrent permeator. (After Walawender and Stem (1972).)... 

We will follow here the treatment of countercurrent gas permeation for a binary mixmre of species A and B as in Section 8.1.9. As shown in Figure 8.2.7 for a cocurrent gas permeator, one can obtain, for species A permeation through membrane area dA over a length dz,... 

Consider a countercurrent gas permeator as well as a cocurrent gas permeator for the separation of a particular binary gas mixture at feed pressure Pf and permeate pressure Pp. Assume that there are no pressure drops on either the feed side or the permeate side. If the pressure ratio y 0, show that the separation achieved would be independent of the flow pattern. Assume a symmetric membrane with constant values of permeances. Will the situation be any different if we used the crossflow permeator of Section 7.2.1.1 ... 

Because of the long, narrow configuration, the equipment appears to function in countercurrent mode. Other data of experiments with gas permeators as continuous columns appear in Figures 19.6(b) and (c) the original paper has data on other binary and some complex mixtures. 

In the case of reverse osmosis, the relative flow configuration does not affect the performance to any large extent. As already indicated, the situation is quite different for gas permeation. While countercurrent flow improves the separation efficiency of hollow fiber modules in reverse osmosis only slightly, as far... 

A commercial gas permeator would probably be close to cross-flow or countercurrent flow (see section 17.71. This would result in more separation than is predicted for the perfecdy mixed system. 

Figure 17-19. Staged models for different flow patterns in gas permeation (A) cross-flow system, (B) co-current system, (C) countercurrent system...

System type (4) Two miscible phases flow countercurrently in two regions of the device separated by a membrane. One of the phases may be generated from one feed phase by the application of pressure energy. Examples include reverse osmosis, ultrafiltration, microflltration, gas permeation, pervaporation. Examples where the other phase is introduced from outside are electrodialysis, dialysis, sweep vapor/ liquid based system. 

In the following part of this section, we provide simple mathematical descriptions of a few common features of two-phase/two-region countercurrent devices, specifically some general considerations on equations of change, operating lines and multicomponent separation capability. Sections 8.1.2, 8.1.3, 8.1.4, 8.1.5 and 8.1.6 cover two-phase systems of gas-Uquid absorption, distillation, solvent extraction, melt crystallization and adsorption/SMB. Sections 8.1.7, 8.1.8 and 8.1.9 consider the countercurrent membrane processes of dialysis (and electrodialysis), liquid membrane separation and gas permeation. Tbe subsequent sections cover very briefly the processes in gas centrifuge and thermal diffusion. 

In earlier chapters we have studied gas separation via gas permeation in two permeator configurations in a completely mixed membrane gas permeation cell (Section 6.4.2.2) in crossflow membrane permeators (Section 7.2.1.1). In the shell-side fed hollow fiber gas permeator of Figure 7.2.1(d), if the permeate is withdrawn from the fiber bore at the feed end only (the other end is closed), then we have countercurrent flow between the feed side and the permeate side. We consider such a gas permeator configuration here via Figure 8.1.51(a) this figure does not show a hollow fiber. However, one could easily model a hollow fiber permeator with the permeate side being the fiber bore (I.D., dj O.D. do). We wiU now develop the governing balance equations for the countercurrent gas... 

The analysis of spirally wound gas permeation devices shown in Figure 7.2.1(e) will not follow the traditional countercurrent analysis formalism. See Ptm (1983, 1986). 

Air is commonly run with tube-side feed. The permeate is run countercurrent with the separating sldn in contact with the permeate. (The feed gas is in contact with the macroporous back side of the membrane.) This configuration has proven to be superior, since the permeate-side mass-transfer problem is reduced to a minimum, and the feed-side mass-transfer problem is not limiting. 

Partial Pressure Pinch An example of the hmitations of the partial pressure pinch is the dehumidification of air by membrane. While O9 is the fast gas in air separation, in this apphcation H9O is faster still. Special dehydration membranes exhibit a = 20,000. As gas passes down the membrane, the pai-dal pressure of H9O drops rapidly in the feed. Since the H9O in the permeate is diluted only by the O9 and N9 permeating simultaneously, p oo rises rapidly in the permeate. Soon there is no driving force. The commercial solution is to take some of the diy air product and introduce it into the permeate side as a countercurrent sweep gas, to dilute the permeate and lower the H9O partial pressure. It is in effect the introduction of a leak into the membrane, but it is a controlled leak and it is introduced at the optimum position. 

Gas separation performances (H2/n-butane, n-hexane/2-2 dimethylbutane) have been measured using a sweep gas (countercurrent mode) in order to increase the permeation driving force (no differential pressure was used) permeate and retentate compositions (see Figure 2) were analysed using on line gas chromatography. 

Figure 9. H2 ( ) / n-butane ( ) separaticm with the ccxnposite zeolite-alumina membrane (fluxes in the permeate as a function of the tenq>erature). A mixture of hydrogen, n-btitane and nitrogen (12 14 74) was fed in the tube (Fig. 2) with a flow rate of 4.8 1/h. Sweep gas (N2), countercurrent mode, flow rate 4.3 1/h.

For natural permeation combustion, the reactant gas may flow in either the same (cocurrent flow. Fig. 27a) or opposite (countercurrent flow. Fig. 27b) direction as that of combustion wave propagation, and in some cases even in both directions Fig. 27c). One-dimensional flow regimes can be achieved by placing the sample in a quartz tube, which in turn can be closed at one end (Pityulin et al, 1979). In the general case (see Fig. 26), the reactant gas also enters from the side surface, and the process can be described by two- or three-dimensional numerical simulations (cf Ivleva and Shkadinskii, 1981 Dandekar et al., 1990, 1993). In this section, results for the simpler one-dimensional case are analyzed and features of the higher dimensional studies are briefly discussed. 

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