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differential elements in series by partitioning the membrane into j subdivisions with axial positions ranging from i = 1 at z = 0 to i = j + 1 at z = L. The results of our model for the concentration profiles are shown in Figures 6.3 through 6.5 for a ratio of the purge gas flow rates to the feed flow rates at approximately 1.1. The tube and shell-side water concentrations are depicted with solid lines and the interfacial water concentrations are the dashed lines. Figure 6.6 shows that the interfacial resistances on the tube and shell-side do not restrict the rate of mass transport to the same extent as that of the resistance in the membrane itself, meaning the diffusion of water through the membrane is the rate limiting factor in the flux of water from the tube to shell side. At first glance it appears that the concentration gradient is independent of axial position for all feed relative humidities investigated, but upon closer inspection it is evident that the gradient at an axial position of z = 0 is larger than that at z = L. This is verified by the profile of the water flux through the membrane depicted in Figure 6.7. There it can be seen that the water flux decreases along the length of the membrane, and as the relative humidity of the process gas decreases. The corresponding temperature profiles of the membrane are displayed in Fig- ures 6.8 through 6.10 with the tube and shell-side values shown with solid curves while the interfacial values are the dashed curves. Unlike water transport, the mem- brane resistance does not play a significant role in the transfer of energy as opposed to the interfacial resistances, meaning that the temperature profiles are fairly linear. Also, since the purge gas is slightly elevated in temperature due to heat of adsorption effects from the desiccant compared to that in the tubes, the direction of the driving force in terms of shell-side and tube-side values is reversed compared to the water transport. During the experiments we noticed that there was a distinct radial temperature gradient in the membrane apparatus, meaning that the top was warmer than the 114PDF Image | TEMPERATURE SWING ADSORPTION COMPRESSION AND MEMBRANE SEPARATIONS
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