Permeation in Porous Membranes

GAS PERMEATION IN POROUS MEMBRANES 2.2.1 Types of Porous Membranes... 

In order to predict correctly the fluxes of multicomponent mixtures in porous membranes, simplified models based solely on Fields law should be used with care [28]. Often, combinations of several mechanisms control the fluxes, and more sophisticated models are required. A well-known example is the Dusty Gas Model which takes into account contributions of molecular diffusion, Knudsen diffusion, and permeation [29]. This model describes the coupled fluxes of N gaseous components, Ji, as a function of the pressure and total pressure gradients with the following equation ... 

However, in porous membranes, which are used in UF, the viscosity factor of the fluid supply, which in turn is related to temperature and solute concentration, represents a major role in determining the permeate flux. According to Kim et al. [21], except for the anomalous behavior of water, all other solvents show a clear correlation between the increase of flow increased and a decrease of viscosity. According to these authors, this indicates that viscosity is the main factor that influences the flow of solvent through UF membranes. 

The aim of Chapter 5 by Thornton et al. was to give systematic consideration to different types of transport in porous membranes. They developed a new model that allows one to predict the separation outcome for a variety of membranes in which the pore shape, size and composition are known, and conversely to predict pore characteristics with known permeation rates. 

In porous membranes, the permeation happens through their pores and then the transport mechanisms (sieving mechanism and/or Knudsen diffusion) depend on the pore size. In dense membranes, the mass transport takes place by the so-called solu-tion/diffusion mechanism. 

Non-potous/dense membrane Figure 1.3 Schematic drawing of the permeation in porous and dense membranes. 

When the catalyst is coated on the membrane surface or dispersed inside the membrane pores, the membrane body will exhibit catalytic activity and participate directly in chemical reactions. To obtain high performance, the porous membrane should provide high surface area and strong adhesion of the catalyst. The reactants permeate from one side or opposite sides of the membrane into the catalyst layer where reactions take place. The catalyst in porous membranes may benefit from the better transfer and membrane active role in promoting the contact of reactants. An appropriate thickness of the catalytic layer is necessary to enhance the reaction selectivity [20]. 

For the transport of gas mixtures, the generalised Maxwell-Stefan equation (Krishna and WesseUngh, 1997) has been widely adopted to describe multi-component diffusion. Although quantitative descriptions of gas diffusion in various microporous or mesoporous ceramic membranes based on statistical mechanics theory (Oyama et al., 2004) or molecular dynamic simulation (Krishna, 2009) have been reported, the prediction of mixed gas permeation in porous ceramic membranes remains a challenging task, due to the difficulty in generating an accurate description of the porous network of the membrane. 

Another possibility of constructing a chiral membrane system is to prepare a solution of the chiral selector which is retained between two porous membranes, acting as an enantioselective liquid carrier for the transport of one of the enantiomers from the feed solution of the racemate to the receiving side (Fig. 1-5). This system is often referred to as membrane-assisted separation. The selector should not be soluble in the solvent used for the elution of the enantiomers, whose transport is driven by a gradient in concentration or pH between the feed and receiving phases. As a drawback common to all these systems, it should be mentioned that the transport of one enantiomer usually decreases when the enantiomer ratio in the permeate diminishes. Nevertheless, this can be overcome by designing a system where two opposite selectors are used to transport the two enantiomers of a racemic solution simultaneously, as it was already applied in W-tube experiments [171]. 

Non-porous, dense membranes consist of a dense film through which permeats are transported by diffusion under the driving force of a pressure, concentration or electrical potential gradient. The separation of various components of a mixture is related directly to their relative transport rates within the membrane, which are determined by their diffusivity and solubility in the membrane material. Thus, non-porous, dense membranes can separate permeats of similar... 

Membranes exhibiting selectivity for ion permeation are termed electrochemical membranes. These membranes must be distinguished from simple liquid junctions that are often formed in porous diaphragms (see Section 2.5.3) where they only prevent mixing of the two solutions by convection and have no effect on the mobility of the transported ions. It will be seen in Sections 6.2 and 6.3 that the interior of some thick membranes has properties analogous to those of liquid junctions, but that the mobilities of the transported ions are changed. 

In Figure 10.10a, it can be seen that for porous membranes, the partial pressure and concentration profiles vary continuously from the bulk feed to the bulk permeate. This is not the case with nonporous dense membranes, as illustrated in Figure 10.10b. Partial pressure or concentration of the feed liquid just adjacent to the upstream membrane interface is higher than the partial pressure or concentration at the upstream interface. Also, the partial pressure or concentration is higher just downstream of the membrane interface than in the permeate at the interface. The concentrations at the membrane interface and just adjacent to the membrane interface can be related according to an equilibrium partition coefficient KM i. This can be defined as (see Figure 10.10b) ... 

In the third part of the chapter the solid state properties of our block copolymer are examined. The surface energies of these materials are characterized by contact angle measurements. The organization of the polymer chains in the solid state phase is investigated by small-angle X-ray scattering (SAXS) and the gas selectivity of porous membranes coated with these block copolymers is characterized by some preliminary permeation measurements. 

The main emphasis in this chapter is on the use of membranes for separations in liquid systems. As discussed by Koros and Chern(30) and Kesting and Fritzsche(31), gas mixtures may also be separated by membranes and both porous and non-porous membranes may be used. In the former case, Knudsen flow can result in separation, though the effect is relatively small. Much better separation is achieved with non-porous polymer membranes where the transport mechanism is based on sorption and diffusion. As for reverse osmosis and pervaporation, the transport equations for gas permeation through dense polymer membranes are based on Fick s Law, material transport being a function of the partial pressure difference across the membrane. 

The situation is somewhat different with porous membranes, where the permselectivities for all components do not equal zero but exhibit certain values determined in most cases by the Knudsen law of molecular masses. In general, when porous membranes are used as separators in a membrane reactor next to the catalyst or the reaction zone (Figure 7.2a), it has been shown experimentally (Yamada et al. 1988) and theoretically (Mohan and Govind 1986, 1988a, b, Itoh et al. 1984, 1985) that there is a maximum equilibrium shift that can be achieved. On the basis of simple mass balances one can calculate that this maximum depends on, besides the reaction mechanism, the membrane permselectivities (the difference in molecular weights of the components to be separated) and it corresponds to an optimum permeation to reaction-rate ratio for the faster permeating component (which is a reaction product). 

Microporous membranes (pore radius less than 10 A) are ideal materials to be used as separators in membrane reactor processes. Microporous membranes also combine the high selectivities to certain components with high permeation rates. The high selectivities mean that maximum conversions (and thus equilibria shifts) higher than those achieved by porous membranes can be attained, while the high permeation rates allow for high reaction rates... 

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