Overall Permeation Reduction Coefficient

According to their definitions, CPC and IC provide quantitative measures of the flux decrease due to concentration polarization and inhibition, respectively. However, it is sometimes useful to have an indication of the overall flux 

For this aim, an overall permeance reduction coelScient , PRCP was introduced, to take into account the permeation reduction owing to both concentration polarization and inhibition at the same time. Its definition, reported in eqn (14.19), arises from the simple consideration that the lowest permeance is evaluated at bulk conditions when both polarization and inhibition affect the membrane system, whereas, on the other hand, the ideal membrane behavior and the maximum permeance can be found under pure hydrogen conditions  

Therefore, it represents the distance of the actual system status from the best possible conditions, providing an immediate quantitative measure of the membrane performance loss. Since, due to its nature, this coefficient takes into account polarization and inhibition, it can be expressed in terms of the other two coefficients, CPC and 7C, by combining eqns (14.13), (14.14) and (14.19) to obtain eqn (14.20)  

From these equations, it is clearly shown that the effects of polarization and inhibition are not simply additive, but are coupled to each other in a more complex relation. In particular, analyzing the second expression in eqn (14.20), it is possible to notice that the second-order term CPC IC is subtractive. This remarkable fact is not only a mere mathematical aspect, but represents a very important physical aspect. 

In fact, as mentioned above, when polarization and inhibition occur at the same time, the presence of inhibition causes the flux to be lower that that measured with polarization only. Since the effect of polarization itself is larger at higher permeating flux, the overall reduction is less than the sum of the two 

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