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between the measured data point and the time averaged value for the entire length of the experiment. The errors associated with the uncertainties in measurements were less than 2% and 3% for pressure and relative humidity, respectively. The propagation of uncertainties in measurements in calculated quantities was then determined using7 ∂ q 2 ∂ q 2 δq= ∂xδx +···+ ∂zδz (5.15) where q is a calculated value, δq is the error in a calculated value, and δx and δz are the errors associated with the measured values. Using this method, all cumulative errors associated with the calculation of water concentrations in the tube and shell sides were determined to be ±5%. Concentration profiles along the length of the membrane for a feed relative humidity of 20% are shown in Figures 5.4 through 5.6 for varying tube-side flow rates of 5, 8, and 10 slpm, respectively. The tube and shell side concentrations are represented by solid curves and the tube-side interfacial concentrations are described by dashed curves. Here it can be seen that the tube side concentration decreases in quantity as the gas stream flows down the length of the membrane, while the shell-side concentration remains constant since we assume that the partial pressure of water on the shell side is uniform and equal to the outlet pressure. Also, the tube-side interfacial resistance does not appear to have a significant impact on the transport of water as much as the resistance through the membrane itself, shown in Figure 5.7, indicating that the diffusion of water through the membrane is the rate limiting factor. It is also important to note that the slope of the concentration profile on the tube side, i.e., dctw/dz is the steepest near the inlet for a tube-side flow rate of 5 slpm. The concentration profiles along the length of the membrane for feed relative humidities of 50% and 70% are shown in Figures 5.8 through 5.10 and Figures 5.11 through 5.13, respectively. As seen in the previous figures, water transport is affected primarily by diffusional resistances of water through the membrane for all feed relative 84PDF Image | TEMPERATURE SWING ADSORPTION COMPRESSION AND MEMBRANE SEPARATIONS
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