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dew point sensor in conjunction with a thermocouple was used upstream of the shell- side inlet. Finally, as the purge gas exited, the flow rate, temperature and pressure were measured once again. Two valves are connected to the membrane apparatus in order to change the flow rate of the purge gas and to maintain a constant back pressure. 6.3 Mathematical Model We examine mass and energy transfer in a water selective shell and tube mem- brane under counter-current operation. A representative schematic of the membrane modeled is shown in Figure 6.2. A humid air stream that is to be dehydrated is fed to the tube side of the membrane at room temperature, while a dry purge gas stream enters the shell side at the opposite end. As the air stream flows through the length of the membrane, water selectively permeates from the tubes to the shell and is swept out by the purge gas. We assume that only water vapor permeates as experiments have shown that permeation rates through Nafion of oxygen and nitrogen were several orders of magnitude lower than that of water. We also assume that axial diffusion is negligible compared with the bulk flow, the process and purge gases may be treated as ideal, the system is adiabatic, and the end effects of the membrane are negligible. Mass transfer We write an overall material balance for the membrane in the form NFtot(y | −y | )=Ftot(y | −y | ) (6.1) t t twz=L twz=0 s swz=0 swz=L where N is the number of tubes in the membrane, Ftot is the total molar flow rate tt per tube, F tot is the total molar flow rate in the shell, and y and y are the position s tw sw dependent mole fractions of water inside the tube and shell respectively. We let F air F air Ftot = t Ftot = s (6.2) t (1−ytw) s (1−ysw) 107PDF Image | TEMPERATURE SWING ADSORPTION COMPRESSION AND MEMBRANE SEPARATIONS
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