Permeate-side concentration

Although less discussed in the technical and scientific literature, permeate-side concentration polarisation may also become a problem when using thin selective films that require macroporous supports for mechanical stability [13]. 

Figure 4.19(a) shows the concentration of water vapor on the feed and permeate sides of the membrane module in the case of a simple counter-flow module. On the high-pressure side of the module, the water vapor concentration in the feed gas drops from 1000 ppm to about 310 ppm halfway through the module and to 100 ppm at the residue end. The graph directly below the module drawing shows the theoretical maximum concentration of water vapor on the permeate side of the membrane. This maximum is determined by the feed-to-permeate pressure ratio of 20 as described in the footnote to page 186. The actual calculated permeate-side concentration is also shown. The difference between these two lines is a measure of the driving force for water vapor transport across the membrane. At the feed end of the module, this difference is about 1000 ppm, but at the permeate end the difference is only about 100 ppm. 

An illustrative example for permeate-side concentration polarization is the per-vaporation of vanillin, a high-boiling aroma compound. The boiling point of vanillin is about 558 K and its saturation vapor pressure correspondingly low (0.29 Pa at... 

Quantity Feed or high-pressure side Permeate or iow-pressure side Concentrate, etc. 

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. 

A phenomenon that is particularly important in the design of reverse osmosis units is that of concentration polarization. This occurs on the feed-side (concentrated side) of the reverse osmosis membrane. Because the solute cannot permeate through the membrane, the concentration of the solute in the liquid adjacent to the surface of the membrane is greater than that in the bulk of the fluid. This difference causes mass transfer of solute by diffusion from the membrane surface back to the bulk liquid. The rate of diffusion back into the bulk fluid depends on the mass transfer coefficient for the boundary layer on feed-side. Concentration polarization is the ratio of the solute concentration at the membrane surface to the solute concentration in the bulk stream. Concentration polarization causes the flux of solvent to decrease since the osmotic pressure increases as the boundary layer concentration increases and the overall driving force (AP - An) decreases. 

The composition at the permeate-phase interface depends on the partial pressure and saturation vapour pressure of the component. Solvent composition within the membrane may vary considerably between the feed and permeate sides interface in pervaporation. By lowering the pressure at the permeate side, very low concentrations can be achieved while the solvent concentration on the feed-side can be up to 90 per cent by mass. Thus, in contrast to reverse osmosis, where such differences are not observed in practice, the modelling of material transport in pervaporation must take into account the concentration dependence of the diffusion coefficients. 

Figure 19.3 schematically describes in more detail the transport phenomena occurring during pervaporation. First, solutes partition into the membrane material according to the thermodynamic equilibrium at the liquid-membrane interface (Fig. 19.3a), followed by diffusion across the membrane material owing to the concentration gradient (Fig. 19.3b). A vacuum or carrier gas stream promotes then continuous desorption of the molecules reaching the permeate side of the membrane (Fig. 19.3c), maintaining in this way a concentration gradient across the membrane and hence a continuous transmembrane flux of compounds.

As before, the exponential term is close to unity thus, the concentration at the permeate side interface is... 

Paul and Paciotti [19] took this work a step further by measuring the flux of a liquid (hexane) through a membrane both in pervaporation experiments with atmospheric pressure on the feed side of the membrane and a vacuum on the permeate side, and in reverse osmosis experiments with liquid at elevated pressures on the feed side and at atmospheric pressure on the permeate side. The hexane flux obtained in these two sets of experiments is plotted in Figure 2.17 against the hexane concentration difference in the membrane (c o(m) — c,eimi). The concentrations, cio(m) and Cie(m), were calculated from Equations (2.26), (2.36) and (2.72). 

Figure 2.17 Flux of n-hexane through a rubbery membrane as a function of the hexane concentration difference in the membrane. Data taken from both reverse osmosis ( ) and pervaporation (O) experiments. Feed-side and permeate-side membrane concentrations, Ci0 m) and Cie m), calculated from the operating conditions through Equations (2.26), (2.36) and (2.76). Maximum flux is obtained at the maximum concentration difference, when the permeate-side membrane concentration cit(m)), equals zero [19]. Reprinted from Driving Force for Hydraulic and Pervaporation Transport in Homogeneous Membranes, D.R. Paul and D.J. Paciotti, J. Polym. Sci., Polym. Phys. Ed. 13, 1201 Copyright 1975. This material is used by permission of John Wiley Sons, Inc.

The results illustrated in Figure 2.16 show that the solvent flux tends towards a limiting value at very high pressures. This value is reached when the concentration of sorbed solvent at the permeate side of the membrane reaches zero, the limiting value. 

The layer of solution immediately adjacent to the membrane surface becomes depleted in the permeating solute on the feed side of the membrane and enriched in this component on the permeate side. Equivalent gradients also form for the other component. This concentration polarization reduces the permeating component s concentration difference across the membrane, thereby lowering its flux and the membrane selectivity. The importance of concentration polarization depends on the membrane separation process. Concentration polarization can significantly affect membrane performance in reverse osmosis, but it is usually well controlled in industrial systems. On the other hand, membrane performance in ultrafiltration, electrodialysis, and some pervaporation processes is seriously affected by concentration polarization. 

Figure 4.1 also shows the formation of concentration polarization gradients on both sides of the membrane. However, in most membrane processes there is a bulk flow of liquid or gas through the membrane, and the permeate-side composition... 

Figure 4.1 shows the concentration gradients that form on either side of a dialysis membrane. However, dialysis differs from most membrane processes in that the volume flow across the membrane is usually small. In processes such as reverse osmosis, ultrafiltration, and gas separation, the volume flow through the membrane from the feed to the permeate side is significant. As a result the permeate concentration is typically determined by the ratio of the fluxes of the components that permeate the membrane. In these processes concentration polarization gradients form only on the feed side of the membrane, as shown in Figure 4.3. This simplifies the description of the phenomenon. The few membrane processes in which a fluid is used to sweep the permeate side of the membrane,...

The salt flux through the membrane is given by the product of the permeate volume flux. /,. and the permeate salt concentration c,p. For dilute liquids the permeate volume flux is within 1 or 2% of the volume flux on the feed side of the membrane because the densities of the two solutions are almost equal. This means that, at steady state, the net salt flux at any point within the boundary layer must also be equal to the permeate salt flux Jvcip. In the boundary layer this net salt flux is also equal to the convective salt flux towards the membrane Jvc, minus the diffusive salt flux away from the membrane expressed by Fick s law (Didcildx). So, from simple mass balance, transport of salt at any point within the boundary layer can be described by the equation... 

In the discussion of concentration polarization to this point, the assumption is made that the volume flux through the membrane is large, so the concentration on the permeate side of the membrane is determined by the ratio of the component fluxes. This assumption is almost always true for liquid separation processes, such as ultrafiltration or reverse osmosis, but must be modified in a few gas separation and pervaporation processes. In these processes, a lateral flow of gas is sometimes used to change the composition of the gas on the permeate side of the membrane. Figure 4.14 illustrates a laboratory gas permeation experiment using this effect. As the pressurized feed gas mixture is passed over the membrane surface, certain components permeate the membrane. On the permeate side of the membrane, a lateral flow of helium or other inert gas sweeps the permeate from the membrane surface. In the absence of the sweep gas, the composition of the gas mixture on the permeate side of the membrane is determined by the flow of components from the feed. If a large flow of sweep gas is used, the partial... 

Figure 4.14 (a) Flow schematic of permeation using a permeate-side sweep gas sometimes used in laboratory gas separation and pervaporation experiments, (b) The concentration gradients that form on the permeate side of the membrane depend on the volume of sweep gas used. In laboratory experiments a large sweep-gas-to-permeate-gas flow ratio is used, so the concentration of permeate at the membrane surface is very low... 

The importance of the pressure ratio in separating gas mixtures can be illustrated by considering the separation of a gas mixture with component concentrations (mol%) nio and njo at a feed pressure of p0. A flow of component across the membrane can only occur if the partial pressure of component i on the feed side of the membrane, is greater than the partial pressure of component i on the permeate side of the membrane, nkpi. That is... 

In the case of the counter-flow/sweep membrane module illustrated in Figure 4.18(c) a portion of the dried residue gas stream is expanded across a valve and used as the permeate-side sweep gas. The separation obtained depends on how much gas is used as a sweep. In the calculation illustrated, 5 % of the residue gas is used as a sweep even so the result is dramatic. The concentration of water vapor in the permeate gas is 13 000 ppm, almost the same as the perfect counter-flow module shown in Figure 4.18(b), but the membrane area required to perform the separation is one-third of the counter-flow case. Mixing separated residue gas with the permeate gas improves the separation The cause of this paradoxical result is illustrated in Figure 4.19 and discussed in a number of papers by Cussler et al. [16]. 

Figure 4.19 The effect of a small permeate-side, counter-flow sweep on the water vapor concentration on the permeate side of a membrane. In this example calculation, the sweep flow reduces the membrane area by two-thirds...

The salt concentration on the permeate side of the membrane can be related to the membrane fluxes by the expression... 

Combining Equations (8.14-8.18) yields an expression linking the concentration of component i on the feed and permeate sides of the membrane... 

The permeate solution metal ion concentration, M, >, does not appear in the flux equation, which means that the membrane metal ion flux is independent of the concentration of metal on the permeate side. However, the flux does depend on the concentration of metal ions, [M]0, on the feed solution side. At low values of [M]c, the flux will increase linearly with [M]c, but at higher concentrations the flux reaches a plateau value as the term [H]C/[M]aK becomes small compared to 1. At this point all of the available carrier molecules are complexed and no further increase in transport rate across the membrane is possible. The form of this dependence is illustrated for the feed and product solution metal ion concentrations in Figure 11.9. 

Pervaporation is a concentration-driven membrane process for liquid feeds. It is based on selective sorption of feed compounds into the membrane phase, as a result of differences in membrane-solvent compatibility, often referred to as solubility in the membrane matrix. The concentration difference (or, in fact, the difference in chemical potential) is obtained by applying a vacuum at the permeate side, so that transport through the membrane matrix occurs by diffusion in a transition from liquid to vapor conditions (Figure 3.1). Alternatively, a sweep gas can be used to obtain low vapor pressures at the permeate side with the same effect of a chemical potential gradient. 

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