Permeate partial pressure

Module design is veiy important for this case, as the high Ot may result in high permeate partial pressure. An example is the separation of HgOTrom air. 

The ratio of the molar fluxes is also the same as the ratio of the permeate partial pressures... 

The second limiting case occurs when the vapor pressure ratio is very large compared to the membrane selectivity. This means that the permeate partial pressure is smaller than the feed partial vapor pressures, and p,e and pje -> 0. Equation (9.11) then becomes... 

Figure 8. CO conversion as a function of the H2 permeate partial pressure for Water-Gas Shift modeling.

Permeate recovery. To achieve high conversions, it is often desirable to maintain a very low permeate partial pressure which leads to an increase in the permeation rate. Vacuum or a sweep gas is usually employed to attain a low permeate pressure. Vacuum adds some energy cost while the use of a sweep gas may require further downstream processing for the recovery of the permeate (if it contains the desired species) or the separation of the permeate from the sweep gas. The use of a condensable gas or vapor as the sweep gas will facilitate the recovery of the permeate. For example, steam can be condensed at a relatively lower temperature and easily separated from many other gases. However, the issue of hydrothermal stability of the membrane, discussed in Chapter 9, can be critical. Air, on the other hand, is a convenient sweep or carrier gas to use because... 

Figure 17 Simulations of transport of a two-component mixture (pi, P2 = 50 kPa) across a zeolitic membrane using the Fickian and Maxwell-Stefan descriptions (Eqs. 5 and 21, respectively). Permeate partial pressures are taken to be zero. The following parameters were used = 0.01 kPa", ...

Figure 5.12 Calculated dependence of hydrogen flux on the hydrogen permeate partial pressure for a Pd—40Cu membrane 15 pm thick. The feed is 65% hydrogen at 115 psia (7.93 bara) total pressure 60% hydrogen recovery (1 bar= 14.5 psi).

The driving force for the permeation of a certain compound A, is given by the difference of its chemical potential between the upstream and the downstream side of the membrane. This difference can be obtained by keeping the partial pressure of the permeating species A-, (Pi = px y,) in the permeate vapour low. Therefore, it is possible to operate at a low total pressure p (the more common choice) or alternatively to use an inert gas carrier to maintain a small value of the mole fraction y,. It is not common to work at a high feed pressure, since the influence of the feed pressure is usually minor, because the chemical potential of a compound in a liquid solution depends only very slightly on this parameter. In theory, a very high feed pressure is only really required if the permeate partial pressure approaches the saturation value. However, it is usually more economic and practical to keep the permeate pressure low or to increase the operative temperature. For these reasons, it is common practice to operate the feed at atmospheric pressure. 

Figure 5.34 Hydrogen partial pressure along the length axis of a membrane tubular reactor operated in parallel (a) and counter-flow (b) arrangements solid lines, retenate partial pressure dashed lines, permeate partial pressure reformate flow rate, 162cm min reformate pressure, 1.36 bar sweep gas flow rate, 40cm min permeate pressure, 1.01 bar left, reaction temperature 300°C right, reaction temperature 500°C [411].

For a binary feed mixture of gases A and B at feed partial pressures of Pf j, and p j, and permeate partial pressures of and pgp respectively, the permeation rates per unit membrane area of the two species are, respectively... 

Although microporous membranes are a topic of research interest, all current commercial gas separations are based on the fourth type of mechanism shown in Figure 36, namely diffusion through dense polymer films. Gas transport through dense polymer membranes is governed by equation 8 where is the flux of component /,andare the partial pressure of the component i on either side of the membrane, /is the membrane thickness, and is a constant called the membrane permeability, which is a measure of the membrane s ability to permeate gas. The ability of a membrane to separate two gases, i and is the ratio of their permeabilities,a, called the membrane selectivity (eq. 9). 

The Permeation Process Barrier polymers limit movement of substances, hereafter called permeants. The movement can be through the polymer or, ia some cases, merely iato the polymer. The overall movement of permeants through a polymer is called permeation, which is a multistep process. First, the permeant molecule coUides with the polymer. Then, it must adsorb to the polymer surface and dissolve iato the polymer bulk. In the polymer, the permeant "hops" or diffuses randomly as its own thermal kinetic energy keeps it moving from vacancy to vacancy while the polymer chains move. The random diffusion yields a net movement from the side of the barrier polymer that is ia contact with a high concentration or partial pressure of the permeant to the side that is ia contact with a low concentration of permeant. After crossing the barrier polymer, the permeant moves to the polymer surface, desorbs, and moves away. 

Equation (22-106) gives a permeate concentration as a function of the feed concentration at a stage cut, 0 = 0, To calculate permeate composition as a function of 0, the equation may be used iteratively if the permeate is unmixed, such as would apply in a test cell. The calculation for real devices must take into account the fact that the driving force is variable due to changes on both sides of the membrane, as partial pressure is a point function, nowhere constant. Using the same caveat, permeation rates may be calciilated component by component using Eq. (22-98) and permeance values. For any real device, both concentration and permeation require iterative calculations dependent on module geometiy. 

Plasticization Gas solubility in the membrane is one of the factors governing its permeation, but the other factor, diffusivity, is not always independent of solubility. If the solubility of a gas in a polymer is too high, plasticization and swelhng result, and the critical structure that controls diffusion selectivity is disrupted. These effects are particularly troublesome with condensable gases, and are most often noticed when the partial pressure of CO9 or H9S is high. H9 and He do not show this effect This problem is well known, but its manifestation is not always immediate. 

Membrane System Design Features For the rate process of permeation to occur, there must be a driving force. For gas separations, that force is partial pressure (or fugacity). Since the ratio of the component fluxes determines the separation, the partial pressure of each component at each point is important. There are three ways of driving the process Either high partial pressure on the feed side (achieved by high total pressure), or low partial pressure on the permeate side, which may be achieved either by vacuum or by introduc-... 

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. 

The quasi-isostatic method is a variation of the isostatic method. In this case at least one chamber is completely closed, and there is no connection with atmospheric pressure. However, there must be a difference in penetrant partial pressure or a concentration gradient between the two cell chambers. The concentration of permeant gas or vapor that has permeated through into the lower-concentration chamber can be quantified by a technique such as gas chromatography (2). 

Process Description Pervaporation is a separation process in which a liquid mixture contacts a nonporous permselective membrane. One component is transported through the membrane preferentially. It evaporates on the downstream side of the membrane leaving as a vapor. The name is a contraction of permeation and evaporation. Permeation is induced by lowering partial pressure of the permeating component, usually by vacuum or occasionally with a sweep gas. The permeate is then condensed or recovered. Thus, three steps are necessary Sorption of the permeating components into the membrane, diffusive transport across the nonporous membrane, then desorption into the permeate space, with a heat effect. Pervaporation membranes are chosen for high selectivity, and the permeate is often highly purified. 

An internally-staged, gas-permeation module is used for the oxygen enrichment of air, using the flow arrangement shown in Fig. 5.206. Enrichment depends on differing membrane permeabilities for the oxygen and nitrogen to be separated. The permeation rates are proportional to the differences in component partial pressures. 

The permeation rates are written in terms of partial pressures, permeabilities, membrane areas and thicknesses as follows ... 

Membranes act as a semipermeable barrier between two phases to create a separation by controlling the rate of movement of species across the membrane. The separation can involve two gas (vapor) phases, two liquid phases or a vapor and a liquid phase. The feed mixture is separated into a retentate, which is the part of the feed that does not pass through the membrane, and a permeate, which is that part of the feed that passes through the membrane. The driving force for separation using a membrane is partial pressure in the case of a gas or vapor and concentration in the case of a liquid. Differences in partial pressure and concentration across the membrane are usually created by the imposition of a pressure differential across the membrane. However, driving force for liquid separations can be also created by the use of a solvent on the permeate side of the membrane to create a concentration difference, or an electrical field when the solute is ionic. 

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