Sieverts driving force

Figure 13.5 H2 flux as function of Sieverts driving force. Scheme summarizing dilution and inhibition effects owing to inert and inhibitor species present in mixture with hydrogen.

Since Sieverts law is valid or the deviation from it is small in most of the operating conditions under which the Pd-based membranes work, the square root difference of hydrogen partial pressure (Sieverts driving force) seems a good choice for the characteristic driving force to define the concentration polarization coefficient. 

The simulation results obtained were reported in terms of polarization maps, which were developed in order for CPC to be read directly and used under the considered operating conditions to estimate the transmembrane flux once the intrinsic membrane permeance and Sieverts driving force of bulk are known (eqn (14.12)). The results from the model solution have been confirmed by a comparison with the experimental ones in order to validate the analysis ... 

The equation used to describe flux is derived from a combination of Pick s and Sieverts laws where the difference between the square root of hydrogen partial pressure on the feed and permeate sides of the membrane creates the driving force for hydrogen flux [168,169] ... 

For Pd-alloy membranes, Sievert s law (eqn (12.1)) is used worldwide for the mathematical description of H2 permeating flux in these types of membranes. The hydrogen permeating flux is a linear function of the permeability and driving force and reverse function of the membrane thickness. The permeation... 

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 ... 

In this equation, whose development and implications will be analyzed in detail throughout this chapter, the only quantity necessary to calculate the flux is justly PRC, since intrinsic Sieverts permeance - i.e. the one not affected by inhibition and/or polarization - and bulk driving force can be simply evaluated from experimental data. 

This particular choice of driving force is not a limitation and does not affect the generality of this approach. In fact, CPC can be calculated for each operating condition, even for those where Sieverts law is not strictly valid. In practice, CPC represent an ignorance correction factor by means of which it is possible to continue to use Sieverts law even when diffusion in the selective metal layer is not the rate-determining step anymore. 

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. 

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