Activation energy permeation equation

The permeability varies with temperature according to equation 12 where is a constant, E is the activation energy for permeation, E. is the gas constant, and Tis the absolute temperature. 

Note that K-cjg t is the Henry constant b as given in Eq. (9.16a) (mol kg Pa" or mol m" Pa" ) which can be directly determined from experiments without separate knowledge of the value of qgaf Equation (9.47) shows that the flux / is activated with an apparent activation energy (E, - Qa ) which is determined directly from permeation experiments. Since both parameters are positive quantities, positive as well as negative values can be expected and the flux can be increase as well as decrease with temperature depending on the relative values of Ej,- and Equation (9.47) has been used by several authors to describe, analyse and/or simulate permeation and diffusion in silica [59,63,92] and in zeolite membranes [69,72,75]. ... 

Equation (9.48c) shows that at high values of 0 (low temperature) the apparent activation energy of the permeation equals that of the diffusivity provided that intra-crystalline diffusion is still the controlling mechanism. 

When the solution-diffusion mechanism is applicable, permeation can usually be treated as an activated process, as described by Equation 15.3. The activation energy Ep changes as the polymer goes through major transitions such as the glass transition or melting. Pq is a pre-exponential factor which has the same units as P(T). 

The hydrogen permeation rate through the palladium membranes follows Richardson s equation, where the values of the apparent activation energy Ea and pre-exponential factor Pe are 12 540 J mol and 2.21 x 10 ° mol s m Pa °, respectively (experimentally determined). 

In order to compare the performance for polymeric and carbon membranes, Figure 15.13 shows a CO2/CH4 trade-offline for P84 and Matrimid precursors and their carbon membranes as reported by Tin et al It is clear that carbon membranes possess excellent permeation properties, where both of the permeability and ideal selectivity access the Robeson upper-bound curve. Moreover, some researchers have also investigated the influence of temperature on the gas permeability.They concluded that the gas permeability values increased with the increase of temperature due to the activated process for the CMS membranes. They also found that the apparent activation energies for CO2 calculated from the Arrhenius equation Pe = Peo Qxp(-EJRT)) was much smaller than the other gas species of O2, N2 and CH4, thereby indicating that CO2 has much higher permeability. 

Figures 7,8 show that the arrhenius plots are linear for all polymers in measurements, and the activation energies of permeation, Ep, were calculated from the data of these Figures, using the following equation.

To describe the module performance mass, energy and momentum balances have to be solved. The mass balance is determined for each component in the gas mixture. The balances calculated for the feed and permeate side are coupled using a mass transfer equation which depends on the operating conditions as well as on membrane characteristics. Assuming Henry sorption, non-coupling of permeate fluxes and equality of the chemical potential at the surface of the active membrane layer a simplified mass transfer equation can be used ... 

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