Permeation driving force

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. 

Some of the variables that are important for the subsequent discussion are recalled here. The membrane properties are related to the mass transport of the different chemical species through the membrane itself or its separating layer (for an asymmetric or multilayer membrane). Permeability and selectivity were defined for the mass transport by permeation both depend on the membrane nature and morphology that impose the specific transport mechanism driving the permeation of which it is characteristic. Table 13.2 reports the permeability coefficient, selectivity and permeating driving force of some permeation mechanisms. 

Table 13.2 Permeability, selectivity and permeating driving force of some transport mechanisms. 

Transport mechanism Permeability Permeation driving force Selectivity aj, -... 

The permeability value of the specific species (ith) can be evaluated as the ratio of the permeating flux (experimentally measurable) and the gradient of the permeating driving force ... 

Another fundamental aspect of an MR is related to the permeation driving force. Any system with a permeance value different from zero gives permeation in the desired direction under a suitable driving force. It can be generated by means of an appropriate value of feed pressure or using a sweep gas. Figure 13.8 shows the MREC... 

Since the permeance and permeability are always different from zero, no permeation is equivalent to zero permeation driving force, which occurs when the species partial pressures on both membrane sides are equal to each other. It must be noted that the equilibrium conversion of an MR is independent of the permeation law that expresses the penetrant velocity through the membrane materials. 

Production of pure H2 permeate stream (when a pressure difference is used instead of a sweep gas to create the permeation driving force)... 

Mass transfer from bulk to membrane surface is affected by external resistance much more in thin membranes than in thicker ones and, moreover, in the presence of inhibiting species for the membrane, the effective membrane area becomes smaller, thereby causing an additional reduction of the permeating flux. All these phenomena, negative for membrane performances, can cause the validity of Sieverts law (eqn (14.1)) to be compromised because the bulk properties (permeance and permeation driving force) are generally different from those evaluated immediately close to the membrane surfaces ... 

The overall negative effect on membrane performances is that the permeation driving force between the membrane surfaces of upstream and downstream is lower than that between the respective bulks, causing a consequent reduction of flux. A significant presence of concentration polarization can make the advantages of preparing very thin membranes partially useless, because the mass transfer resistance tends to be located in the gas phase external to the membrane rather than in the membrane itself. 

Defining Concentration Polarization Coefificient According to Hydrogen Permeation Driving Force... 

By comparing the expressions in eqn (14.7), this definition can be read in two ways when concentration polarization is negligible, i.e. CPC 0, membrane permeance is, in fact, coincident with that of bulk, or, dually, the permeation driving force between the bulks is the same as that between the membrane surfaces. It should also be noticed that the condition of maximum polarization, i.e. CPC= 1, is an asymptotic conditions where permeating flux tends to zero because the hydrogen partial pressure at membrane surface approaches to zero. This situation is summarized in Table 14.2. 

The results of the DaPe analysis for the above example are reported in the Fig. 16.3. Because the example only includes DaPe values greater than 1, the hydrogen permeated is much less than that produced. The DaPe decreased when the overpotential increased, that is, a higher overpotential involves higher which increases the permeation driving force. 

Membrane process Feed Phase Permeate Driving force Pore size Note... 

A comparison of Equations 13.24 and 13.25 identifies that the term 1/Ka is a mass transfer resistance (rcP s Pa mol ) taking into account surface phenomena or wall effects, leading to deviations from Equation 13.24 [30-32]. In fact, the term //Kd (Pa) introduces a pressure drop reducing the permeation driving force of the Sieverts law of permeation. In other words, the expression 13.24 can be derived from Equation 13.25 by modifying the driving force for the surface effects as shown in Figure 13.11. 

FIGURE 13.11 Permeation driving force of Sieverts expression in the presence of surface effects. 

In the MREF, the methane reacts forming CO, COj, H2O and H2, where the latter can permeate across the membrane and feed the fuel cell. The injection of a sweep gas (in this case steam) decreases the partial pressure of hydrogen on the permeate side of the membrane enhancing the permeation driving force (see Equation [14.34]). The permeation flow is counter-current to the reacting mix in order to have the highest partial pressure difference along the membrane. The assumed inlet velocity profiles are parabolic for sweep gas and hot gas streams, and flat for the feed section. 

Temperature profiles, methane conversion, HRF and permeated flow are shown in Fig. 14.6. Figure 14.7 shows the membrane temperature profile and the permeation driving force along the reactor. Table 14.4 shows the permeation results and the product outcome, outlining that total hydrogen permeated is lower (26%) for the counter-current configuration. The calculated HRF and methane conversion ( CH4 ) in the counter-current flow... 

Comparison of membrane temperature and permeation driving force between co-current and counter-current configurations. 

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