Capillary condensate permeation

Notwithstanding any particular structural model, water transport in PEMs, in general, should be considered a superposition of diffusion in gradients of activity or concentration and hydraulic permeation in gradients of liquid or capillary pressure. Hydraulic permeation is the predominant mechanism xmder conditions for which water uptake is controlled by capillary condensation, whereas diffusion contributes significantly if water strongly interacts with the polymeric host. The molar flux of liquid water in the membrane, N, is thus given by... 

Figure 63. Six flow models for multilayer diffusion and capillaiy condensation (1) multilayer difliision, (2) capillary condensation at feed side. (3) entire pore filled with condensate, (4) bulk condensate at feed side, (5) bulk condensate at feed side and capillary condensate at permeate side and (6) total bulk condensate data taken from Lee and Hwang (1986).

Du 1986). This reflects the importance of smaU pores in order to apply effectively capillary condensation as a separation mechanism. Uhlhom (1990) demonstrated the effect of multilayer diffusion of propylene through a modified y-alumina membrane at 0°C. The separation factor for the N2/CjHg mixture was 27, where propylene is the preferentially permeating component, while the permeability increased to 7 times the Knudsen diffusion permeability. Although this mechanism appears to be very effective because of a high separation factor and a high permeability, it is limited by the obvious need for a condensable component. This in turn restricts the applicability range, due to limits set by temperature and pressure, needed for formation of multilayers or capillary condensation. 

Finally it should be noted that inorganic membranes suitable for separation by multilayer diffusion and capillary condensation are also appropriate for performing pervaporation (a technique in which the feed is liquid and the permeate is gas) and distillation at reduced pressure (where gases with overlapping condensation regions are separated). 

When one of the components can condense within the pores, the capillary condensation mechanism is enabled (Fig. 9). The condensate fills the pores and then evaporates at the permeate side, where a low pressure is imposed [54]. Moreover, the transfer of rather big molecules is generally favored by this mechanism over rather small ones. Provided the pore dimension is small and homogeneous enough, and the pores themselves uniformly dispersed over the membrane, this mechanism allows for very high selectivities (separation factors between 80 and 10(X), as reported in [55]) limited only by the solubility of noncondensable molecules in the condensate. However, capillary forces are strong enough to promote this mechanism only with small pore sizes at relatively low temperatures. Hence, as for surface or multilayer diffusion, the practical chances of application appear poor in inorganic-membrane reactors. 

In this case the permeation is proportional to the average pore radius r and inversely proportional to but is independent of the mean pressure P that is an important difference from viscous flow. The separation selectivity between two gases will be proportional to M2/M-[f. In the case of vapor transport in mesopores, another mechanism that may occur is the capillary condensation leading to selective filling of pores by a molecule and preferential transport of this molecule. 

Transfer mechanisms involved in SC CO2 permeation through such porous membranes can be convection (Poiseuille law), diffusion (Knudsen flow), and surface membrane interaction by adsorption, capillary condensation, etc. [11]. Mechanisms have been specifically investigated for nanofiltration and zeolite membranes. With a nanofilter presenting a pore diameter of about 1 nm, Sarrade [11] mentioned a Poiseuille flow associated with an irreversible CO2 adsorption on the micropore wall. Transfer... 

A few publications have reported the permeation of capillary condensate in mesoporous materials. Caiman and Raal [14], measured permeability of CFiCb in Linde silica porous plugs at 240 and 251.5 K. Lee and Hwang [15], measured freon and water vapor permeabilities on vycor membranes. These permeabilities were found to exhibit maxima at relative pressures around 0.6-0.8, with values 20-50 times the Knudsen permeability. Ulhom et al. [16], reported a similar behavior for propylene at 263K in y-alumina membranes. Sperry et al. [17] demonstrated the ability of mesoporous y-alumina membranes in methanol separation at 473 K, provided the applied pressure... 

For practical applications a combination of high selectivity and high permeation is required. As will be shown below, these two requirements are more or less contradictory and so an optimal compromise has to be sought. In this chapter a certain focus will be given to mechanisms with a large potential for high separation factors and at least reasonable permeation values. This leads to microporous systems or capillary condensation type of phenomena. 

A schematic picture of different t5q)es of pores is given in Fig. 9.1 and of main types of pore shapes in Fig. 9.2. In single crystal zeolites the pore characteristics are an intrinsic property of the crystalline lattice [3] but in zeolite membranes other pore types also occur. As can be seen from Fig. 9.1, isolated pores and dead ends do not contribute to the permeation under steady conditions. With adsorbing gases, dead end pores can contribute however in transient measurements [1,2,3]. Dead ends do also contribute to the porosity as measured by adsorption techniques but do not contribute to the effective porosity in permeation. Pore shapes are channel-like or slit-shaped. Pore constrictions are important for flow resistance, especially when capillary condensation and surface diffusion phenomena occur in systems with a relatively large internal surface area. 

An extensive analysis of data and theories describing permeation by surface flow and capillary condensation is given by Uhlhorn [21a]. A fully satisfactory explanation of surface flow mechanisms has not been provided. Some very useful models and equations are however available and will be discussed below. 

Fig. 9.8. Schematic picture of the permeation as a function of the relative pressure in the presence of capillary condensate. After Uhlhom et al. [21]. (1) Onset of multilayer adsorption (2) pores are...

The gas is applied as a mixture to the retentate (high pressure) side of the membrane, the components of the mixture diffuse with different rates through the membrane under the action of a total pressure gradient and are removed at the permeate side by a sweep gas or by vacuum suction. Because the only segregative mechanisms in mesopores are Knudsen diffusion and surface diffusion/capillary condensation (see Table 9.1), viscous flow and continuum (bulk gas) diffusion should be absent in the separation layer. Only the transition state between Knudsen diffusion and continuum diffusion is allowed to some extent, but is not preferred because the selectivity is decreased. Nevertheless, continuum diffusion and viscous flow usually occur in the macroscopic pores of the support of the separation layer in asymmetric systems (see Fig. 9.2) and this can affect the separation factor. Furthermore the experimental set-up as shown in Fig. 9.11 can be used vmder isobaric conditions (only partial pressure differences are present) for the measurement of diffusivities in gas mixtures in so-called Wicke-Callenbach types of measurement. 

The permeation of gases in membranes due to surface diffusion and capillary condensation has been discussed in Section 9.2.3.S. together with some illustrative data. The total flux of a single gas is usually calculated as the sum of the flux by surface diffusion and the flux through the gas phase. As shown the surface flux can contribute considerably to the total flux (increased by factor 2-3 of gas diffusional flux), especially with smaller and uniform pore sizes (compare Eqs. (9.9a) and (9.15). With decreasing pore size the flux through the bulk gas decreases while the surface diffusional flux increases. With very small pore diameter (< 2-3 nm) the effective diameter for bulk gas transport is less than the geometric pore diameter due to the thickness of the absorbed layer which... 

Brief overviews are given by Keizer et al. [50] and Sperry et al. [39] and these show that very high separation factors in combination with large permeation can be obtained in cases of mixtures of an easily condensable gas (vapour) and a difficult (non)-condensable gas which has a low solubility in the condensed phase. Pore blocking by capillary condensation takes place at 0.5-0.8 of the saturated vapour pressure (depending on pore size) and is preceded by multilayer diffu-... 

A type of pore blocking by one of the components occurs but whether this is capillary condensation is not certain. Asaeda and Du [38] reported values up to a > 100 for water-light-alcohol mixtures at 70-90°C in cilumina-silica membranes. The water permeability is dependent on its concentration in the mixture. At atmospheric pressure and 20% water a typical water permeation vcdue is 1.3x10 m s (= 20 1 H2O (liquid) m" day ). Azeotropic points can be bypassed in this way with an alcohol concentration much higher than the azeotropic concentration. 

Permeation is measured at relative pressure p/po where pore is filled (capillary condensation). po is condensation (saturation pressure) of free liquid. 

Pressure loss on the permeate side results in an increase in partial pressure and hence in a decrease in driving force and flux. When the pores are too small, the pressure loss may be so high that even capillary condensation may occur. On the other hand, if the pores in the support layer are too large it is difficult to apply a thin selective layer directly... 

It should be emphasized again that hydraulic permeation models do not rule out water transport by diffusion. Both mechanisms contribute concurrently. The water content in the PEM determines relative contributions of diffusion and hydraulic permeation to the total backflux of water. Hydraulic permeation prevails at high water contents, that is, under conditions for which water uptake is controlled by capillary condensation. Diffusion prevails at low water contents, that is, under conditions for which water strongly interacts with the polymeric host (chemisorption). The critical water content that marks the transition from diffusion-dominated to hydraulic permeation-dominated transport depends on water-polymer interactions and porous network morphology. Sorption experiments and water flux experiments suggest that this transition occurs at A. 3 for Nafion with equivalent weight 1100. 

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